Download or read book Mean Curvature Flow and Isoperimetric Inequalities written by Manuel Ritoré and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Download or read book Mean Curvature Flow written by Theodora Bourni and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-12-07 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.
Download or read book Isoperimetric Inequalities in Riemannian Manifolds written by Manuel Ritoré and published by Springer Nature. This book was released on 2023-10-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Download or read book Isoperimetric Inequalities in the Theory of Surfaces of Bounded External Curvature written by Iurii D. Burago and published by Springer. This book was released on 1970 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Isoperimetric Inequalities written by Isaac Chavel and published by Cambridge University Press. This book was released on 2001-07-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Download or read book Isoperimetric Inequalities and Applications written by Catherine Bandle and published by Pitman Publishing. This book was released on 1980 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes on Mean Curvature Flow written by Carlo Mantegazza and published by Springer Science & Business Media. This book was released on 2011-07-28 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.
Download or read book Analytic Aspects of Convexity written by Gabriele Bianchi and published by Springer. This book was released on 2018-02-28 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.
Download or read book Regularity Theory for Mean Curvature Flow written by Klaus Ecker and published by Springer Science & Business Media. This book was released on 2004 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
Download or read book Space Time Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Download or read book Mathematics Unlimited 2001 and Beyond written by Björn Engquist and published by Springer. This book was released on 2017-04-05 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Download or read book Regularity Theory for Mean Curvature Flow written by Klaus Ecker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
Download or read book An Introduction to the Heisenberg Group and the Sub Riemannian Isoperimetric Problem written by Luca Capogna and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
Download or read book Minimal Surfaces Integrable Systems and Visualisation written by Tim Hoffmann and published by Springer Nature. This book was released on 2021-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.
Download or read book Comparison Geometry written by Karsten Grove and published by Cambridge University Press. This book was released on 1997-05-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.
Download or read book Wave Motion Theory Modelling and Computation written by AlexandreJ. Chorin and published by Springer. This book was released on 1987-10-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 60th birthday of Peter Lax was celebrated at Berkeley by a conference entitled Wave Motion: theory, application and computation held at the mathematical Sciences Research Institute, June 9-12, 1986. Peter Lax has made profound and essential contributions to the topics described by the title of the conference, and has also contributed in important ways to many other mathematical subjects, and as a result this conference volume dedicated to him includes research work on a variety of topics, not all clearly related to its title.
Download or read book 2019 20 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2021-02-10 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
