端点流形上的庞卡罗常数

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2022-05-12 DOI:10.1112/plms.12522

A. Grigor’yan, Satoshi Ishiwata, L. Saloff‐Coste

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引用次数: 1

摘要

我们得到了具有有限多个末端的流形上中心球的庞加莱常数的最优估计。令人惊讶的是，庞加莱常数是由第二大端决定的。该证明基于Kusuoka–Stroock的论点，其中对中心球的热核估计起着至关重要的作用。为此，我们将作者获得的早期热核估计扩展到一类更大的带端抛物流形。

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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Poincaré constant on manifolds with ends

We obtain optimal estimates of the Poincaré constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincaré constant is determined by the second largest end. The proof is based on the argument by Kusuoka–Stroock where the heat kernel estimates on the central balls play an essential role. For this purpose, we extend earlier heat kernel estimates obtained by the authors to a larger class of parabolic manifolds with ends.

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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.