Download or read book New Complex Analytic Methods in the Study of Non Orientable Minimal Surfaces in Rn written by Antonio Alarcón and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
Download or read book Minimal Surfaces from a Complex Analytic Viewpoint written by Antonio Alarcón and published by Springer Nature. This book was released on 2021-03-10 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Download or read book New Complex Analytic Methods in the Study of Non Orientable Minimal Surfaces in Mathbb R n written by Antonio Alarcón and published by . This book was released on 2020 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in \mathbb{R}^n for any n\ge 3. These methods, which the authors develop essentially from the first principles, enable them to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to \mathbb{R}^n is a real analytic Banach manifold, obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces, and show general position theorems for non-orientable co.
Download or read book Global Smooth Solutions for the Inviscid SQG Equation written by Angel Castro and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
Download or read book Dynamics Near the Subcritical Transition of the 3D Couette Flow I Below Threshold Case written by Jacob Bedrossian and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
Download or read book The Riesz Transform of Codimension Smaller Than One and the Wolff Energy written by Benjamin Jaye and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
Download or read book Conformal Graph Directed Markov Systems on Carnot Groups written by Vasileios Chousionis and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
Download or read book Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.
Download or read book Filtrations and Buildings written by Christophe Cornut and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.
Download or read book Differential Function Spectra the Differential Becker Gottlieb Transfer and Applications to Differential Algebraic K Theory written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Download or read book Operator Theory on One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus and Spectral Operators written by Jonathan Gantner and published by American Mathematical Society. This book was released on 2021-02-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Download or read book ojasiewicz Simon Gradient Inequalities for Coupled Yang Mills Energy Functionals written by Paul M Feehan and published by American Mathematical Society. This book was released on 2021-02-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Download or read book Gromov Witten Theory of Quotients of Fermat Calabi Yau Varieties written by Hiroshi Iritani and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Resolvent Heat Kernel and Torsion under Degeneration to Fibered Cusps written by Pierre Albin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Download or read book Local Well Posedness and Break Down Criterion of the Incompressible Euler Equations with Free Boundary written by Chao Wang and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
