A Poincaré Formula for Differential Forms and Applications

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-08 DOI:10.3842/sigma.2023.088

Nicolas Ginoux, Georges Habib, Simon Raulot

引用次数: 0

Abstract

We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived assuming the existence of a nonzero parallel form on the manifold.

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微分形式的poincarcars公式及其应用

在非空边界紧黎曼流形上证明了微分形式的一个新的一般poincar型不等式。当边界等距浸入欧几里德空间时，我们导出了一个只涉及边界的平均曲率和标量曲率的不等式，并刻画了它在余维1上的极限情况。在流形上存在非零平行形式的前提下，导出了微分形式下的一个新的ros型不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.