Surgery and positive Bakry-Émery Ricci curvature.

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2026-01-01 Epub Date: 2026-01-12 DOI:10.1007/s00526-025-03211-2

Philipp Reiser, Francesca Tripaldi

引用次数: 0

Abstract

We consider the problem of preserving weighted Riemannian metrics of positive Bakry-Émery Ricci curvature along surgery. We establish two theorems of this type: One for connected sums, and one for surgeries along higher-dimensional spheres. In contrast to known surgery results for positive Ricci curvature, these results are local, i.e. we only impose assumptions on the weighted metric locally around the sphere along which the surgery is performed. As application we then show that all closed, simply-connected spin 5-manifolds admit a weighted Riemannian metric of positive Bakry-Émery Ricci curvature. By a result of Lott, this also provides new examples of manifolds with a Riemannian metric of positive Ricci curvature.

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手术和阳性的Bakry-Émery Ricci曲度。

我们考虑沿手术方向保留正Bakry-Émery Ricci曲率的加权黎曼度量的问题。我们建立了这类的两个定理：一个是关于连通和的，另一个是关于沿高维球面的手术的。与已知的正里奇曲率的手术结果相反，这些结果是局部的，即我们只在手术进行的球体周围的局部加权度规上施加假设。作为应用，我们证明了所有闭合单连通自旋5流形都具有正Bakry-Émery Ricci曲率的加权黎曼度规。通过洛特的结果，这也提供了具有正里奇曲率黎曼度规的流形的新例子。

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

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.