Degree Theory Of Immersed Hypersurfaces

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Degree Theory Of Immersed Hypersurfaces

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Author : Harold Rosenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Degree Theory Of Immersed Hypersurfaces written by Harold Rosenberg 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 degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.

Degree Theory Of Immersed Hypersurfaces

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Author : Harold Rosenberg
language : en
Publisher:
Release Date : 2011

Degree Theory Of Immersed Hypersurfaces written by Harold Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Conformal Symmetry Breaking Differential Operators On Differential Forms

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Author : Matthias Fischmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Conformal Symmetry Breaking Differential Operators On Differential Forms written by Matthias Fischmann 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 2021-06-18 with Education categories.

We study conformal symmetry breaking differential operators which map dif-ferential forms on Rn to differential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules for so(n +1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, d¯ and δ¯ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover opera- tors of the Euclidean metrics on Rn and Rn−1 and the operators d, δ, d¯ and δ¯ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn−1, respectively.

General Existence Theorems In Moduli Theory

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Author : Jack Kingsbury Hall
language : en
Publisher: Stanford University
Release Date : 2011

General Existence Theorems In Moduli Theory written by Jack Kingsbury Hall and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

In this thesis, we prove that there is an algebraic stack parameterizing all curves. The curves that appear in this algebraic stack are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also prove the boundedness of the open substack parameterizing reduced and connected curves with fixed arithmetic genus g and at most e irreducible components. We also show that for essentially any algebraic stack, there is an algebraic stack, the Hilbert stack, parameterizing quasi-finite maps to the stack. The technical heart of this result is a generalization of formal GAGA to a non-separated morphism of algebraic stacks, something that was previously unknown for a morphism of schemes. We also employ derived algebraic geometry, in an essential way, to prove the algebraicity of the Hilbert stack. The Hilbert stack, for algebraic spaces, was claimed to exist by M. Artin (1974), but was left unproved due to a lack of foundational results for non-separated algebraic spaces. Finally, we generalize the fundamental GAGA results of J. P. Serre (1956) in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of the moduli stack of smooth curves possessing modular interpretations are algebraizable.

Critical Point Theory And Submanifold Geometry

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Author : Richard S. Palais
language : en
Publisher: Springer
Release Date : 2006-11-14

Critical Point Theory And Submanifold Geometry written by Richard S. Palais and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Real And Complex Submanifolds

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Author : Young Jin Suh
language : en
Publisher: Springer
Release Date : 2014-12-05

Real And Complex Submanifolds written by Young Jin Suh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Mathematics categories.

Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10–12, 2014. The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.

Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties

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Author : Hiroshi Iritani
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21

Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties written by Hiroshi Iritani 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.

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.

Theory Of Fundamental Bessel Functions Of High Rank

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Author : Zhi Qi
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10

Theory Of Fundamental Bessel Functions Of High Rank written by Zhi Qi 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.

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.

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.

Weakly Modular Graphs And Nonpositive Curvature

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Author : Jérémie Chalopin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Weakly Modular Graphs And Nonpositive Curvature written by Jérémie Chalopin 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 2021-06-18 with Education categories.

This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated fields of mathematics: * Metric graph theory * Geometric group theory * Incidence geometries and buildings * Theoretical computer science and combinatorial optimization We give a local-to-global characterization of weakly modular graphs and their sub-classes in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With l1–embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT(0) property). Their cells have a specific structure: they are basis polyhedra of even 􀀁–matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme.