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arXiv · 2408.03640

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

Mingxiang Li
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Abstract

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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Mingxiang Li. 2024-08-07. The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II). https://arxiv.org/abs/2408.03640

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