Download or read book The Index Theorem for Minimal Surfaces of Higher Genus written by Friedrich Tomi and published by American Mathematical Soc.. This book was released on 1995 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
Download or read book The Index Theorem for Minimal Surfaces of Higher Genus written by Friedrich Tomi and published by . This book was released on 1995 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Analysis of Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau ́s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
Download or read book Higher Multiplicities and Almost Free Divisors and Complete Intersections written by James Damon and published by American Mathematical Soc.. This book was released on 1996 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost free divisors and complete intersections form a general class of nonisolated hypersurface and completer intersection singularities. They also include discriminants of mappings, bifurcation sets, and certain types of arrangements of hyperplanes such as Coxeter arrangements and generic arrangements. Associated to the singularities of this class is a "singular Milnor fibration" which has the same homotopy properties as the Milnor fibration for isolated singularities. This memoir deduces topological properties of singularities in a number of situations including: complements of hyperplane arrangements, various nonisolated complete intersections, nonlinear arrangements of hypersurfaces, functions on discriminants, singularities defined by compositions of functions, and bifurcation sets.
Download or read book An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces written by Wayne Aitken and published by American Mathematical Soc.. This book was released on 1996 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.
Download or read book Generalized Symplectic Geometries and the Index of Families of Elliptic Problems written by Liviu I. Nicolaescu and published by American Mathematical Soc.. This book was released on 1997 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.
Download or read book Variational Methods for Free Surface Interfaces written by Paul Concus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vallombrosa Center was host during the week September 7-12, 1985 to about 40 mathematicians, physical scientists, and engineers, who share a common interest in free surface phenomena. This volume includes a selection of contributions by participants and also a few papers by interested scientists who were unable to attend in person. Although a proceedings volume cannot recapture entirely the stimulus of personal interaction that ultimately is the best justification for such a gathering, we do offer what we hope is a representative sampling of the contributions, indicating something of the varied and interrelated ways with which these classical but largely unsettled questions are currently being attacked. For the participants, and also for other specialists, the 23 papers that follow should help to establish and to maintain the new ideas and insights that were presented, as active working tools. Much of the material will certainly be of interest also for a broader audience, as it impinges and overlaps with varying directions of scientific development. On behalf of the organizing committee, we thank the speakers for excellent, well-prepared lectures. Additionally, the many lively informal discussions did much to contribute to the success of the conference.
Download or read book Handbook of Differential Geometry Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Download or read book Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable written by Kazuyoshi Kiyohara and published by American Mathematical Soc.. This book was released on 1997 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Download or read book Lie Groups and Subsemigroups with Surjective Exponential Function written by Karl Heinrich Hofmann and published by American Mathematical Soc.. This book was released on 1997 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.
Download or read book Geometry of Loop Spaces and the Cobar Construction written by Hans J. Baues and published by American Mathematical Soc.. This book was released on 1980 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
Download or read book Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball written by Michael A. Dritschel and published by American Mathematical Soc.. This book was released on 1997 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Download or read book Axiomatic Stable Homotopy Theory written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1997 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.
Download or read book Stratifying Endomorphism Algebras written by Edward Cline and published by American Mathematical Soc.. This book was released on 1996 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a systematic study of the relationships between the representation theories of [italic capital]R and [italic capital]A, especially those involving actual or potential quasi-hereditary structures on the latter algebra. Our original motivation comes from the theory of Schur algebras, work of Soergel on the Bernstein-Gelfand-Gelfand category [script capital]O, and resent results of Dlab-Heath-Marko realizing certain endomorphism algebras as quasi-hereditary algebras. We synthesize common features of all these examples, and go beyond them in a number of new directions.
Download or read book Degenerate Principal Series for Symplectic and Odd Orthogonal Groups written by Chris Jantzen and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.
Download or read book Orders of a Quartic Field written by Jin Nakagawa and published by American Mathematical Soc.. This book was released on 1996 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.
Download or read book Symmetric Automorphisms of Free Products written by Darryl McCullough and published by American Mathematical Soc.. This book was released on 1996 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct a complex [italic capital]K([italic capital]G) on which the automorphism group of [italic capital]G acts and use it to derive finiteness consequences for the group [capital Greek]Sigma [italic]Aut([italic capital]G). They prove that each component of [italic capital]K([italic capital]G) is contractible and describe the vertex stabilizers as elementary constructs involving the groups [italic capital]G[subscript italic]i and [italic]Aut([italic capital]G[subscript italic]i).
