vix.ing · top · new · best · stats · spec

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

2024/08/07 by Mingxiang Li, Li, Mingxiang
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2408.03640

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.

Related