New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn
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New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn
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Author : Antonio Alarcón
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn written by Antonio Alarcón and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
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.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
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.
Global Smooth Solutions For The Inviscid Sqg Equation
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Author : Angel Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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.
Filtrations And Buildings
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Author : Christophe Cornut
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Filtrations And Buildings written by Christophe Cornut and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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.
Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case
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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case written by Jacob Bedrossian and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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.
Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields
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Author : Lisa Berger
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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 $mathbb F_q(t^1/d)$.
Conformal Graph Directed Markov Systems On Carnot Groups
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Author : Vasileios Chousionis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Conformal Graph Directed Markov Systems On Carnot Groups written by Vasileios Chousionis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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.
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals
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Author : Paul M Feehan
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals written by Paul M Feehan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
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.
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators
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Author : Jonathan Gantner
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators written by Jonathan Gantner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
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.
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory written by Ulrich Bunke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
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.