总 Q 曲率、体积熵和多项式增长多谐函数 (II)

arXiv - MATH - Differential Geometry Pub Date : 2024-08-07 DOI:arxiv-2408.03640

Mingxiang Li

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引用次数: 0

摘要

这是我们之前工作（《数学进展》450（2024），论文编号 109768）的延续。在本文中，我们将具有无限总 Q 曲率的完全度量表征为所有维度情况下的正常度量。其次，我们引入了另一种体积熵，以提供关于具有有限总 Q 曲率的完全非正态度量的几何信息。我们特别指出，如果标量曲率自下而上是有界的，那么这种完全度量的体积增长就会受到控制。

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The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II)

This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we introduce another volume entropy to provide geometric information regarding complete non-normal metrics with finite total Q-curvature. In particular, we show that if the scalar curvature is bounded from below, the volume growth of such complete metrics is controlled.

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arXiv - MATH - Differential Geometry

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