广义山叶孤子的结构及其应用

Pub Date : 2024-03-07 DOI:10.1017/s0013091524000117

Shun Maeta

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引用次数: 0

摘要

我们考虑的是梯度山边孤子的最广义概念--共形梯度孤子。在本文中，我们在一些假设条件下阐明了完全梯度共形孤子的结构，并提供了梯度山边孤子的一些应用。这些结果加深了人们对以往研究的理解。此外，我们还给出了佩雷尔曼猜想的山边孤子版本的部分肯定答案。

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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Structure of generalized Yamabe solitons and its applications

We consider the broadest concept of the gradient Yamabe soliton, the conformal gradient soliton. In this paper, we elucidate the structure of complete gradient conformal solitons under some assumption, and provide some applications to gradient Yamabe solitons. These results enhance the understanding gained from previous research. Furthermore, we give an affirmative partial answer to the Yamabe soliton version of Perelman’s conjecture.

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