Optimal coordinates for Ricci-flat conifolds

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-22 DOI:10.1007/s00526-024-02780-y

Klaus Kröncke, Áron Szabó

引用次数: 0

Abstract

We compute the indicial roots of the Lichnerowicz Laplacian on Ricci-flat cones and give a detailed description of the corresponding radially homogeneous tensor fields in its kernel. For a Ricci-flat conifold (M, g) which may have asymptotically conical as well as conically singular ends, we compute at each end a lower bound for the order with which the metric converges to the tangent cone. As a special subcase of our result, we show that any Ricci-flat ALE manifold \((M^n,g)\) is of order n and thereby close a small gap in a paper by Cheeger and Tian.

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Ricci-flat conifolds 的最佳坐标

我们计算了 Ricci 平面圆锥上 Lichnerowicz 拉普拉奇的指示根，并详细描述了其内核中相应的径向同质张量场。对于可能有渐近圆锥端和圆锥奇异端的理ci-平面圆锥体（M，g），我们计算了每一端度量收敛到切圆锥的阶次下限。作为我们结果的一个特殊子例，我们证明了任何里奇平坦 ALE 流形（(M^n,g)\）都是 n 阶的，从而弥补了 Cheeger 和 Tian 论文中的一个小漏洞。

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.