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Bull. Korean Math. Soc. 2022; 59(6): 1423-1438

Online first article August 29, 2022      Printed November 30, 2022

https://doi.org/10.4134/BKMS.b210799

Copyright © The Korean Mathematical Society.

Tamed exhaustion functions and Schwarz type lemmas for almost Hermitian manifolds

Weike Yu

Nanjing University of Science and Technology

Abstract

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In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

Keywords: Almost Hermitian manifold, canonical connection, Hessian comparison theorem, tamed exhaustion function, Schwarz lemma

MSC numbers: Primary 32Q60

Supported by: The author is supported by Jiangsu Funding Program for Excellent Postdoctoral Talent (2022ZB281).

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