具有加权p-Poincaré不等式的光滑测度空间上的消灭定理

周久儒

doi:10.13371/j.cnki.chin.q.j.m.2020.03.006

数学季刊 >

2020 , Vol. 35 >Issue 3: 311 - 319

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.03.006

具有加权p-Poincaré不等式的光滑测度空间上的消灭定理

展开

School of Mathematical Sciences, Yangzhou University

ZHOU Jiu-ru(1982-), male, native of Taizhou, Jiangsu, a Lecturer of Yangzhou University, Ph.D, engages in dierential geometry.

收稿日期: 2020-06-01

网络出版日期: 2020-10-22

基金资助

Partially supported by National Science Foundation of China(11426195,11771377)； Natural Science Foundation of Jiangsu Province(BK20191435)；

收起

Vanishing Theorems on Smooth Metric Measure Spaces with a Weighted p-Poincaré Inequality

Expand

School of Mathematical Sciences, Yangzhou University

ZHOU Jiu-ru(1982-), male, native of Taizhou, Jiangsu, a Lecturer of Yangzhou University, Ph.D, engages in dierential geometry.

Received date: 2020-06-01

Online published: 2020-10-22

Supported by

Partially supported by National Science Foundation of China(11426195,11771377)； Natural Science Foundation of Jiangsu Province(BK20191435)；

Fold

摘要

This paper deals with vanishing results for L_f² harmonic p-forms on complete metric measure spaces with a weighted p-Poincaré inequality. Some results are without curvature assumptions for 1 ≤ p ≤ n-1 and the others are with assumptions on lower bound of the m-Bakry-émery Ricci curvature for p = 1. These are weighted version for the corresponding results of the present author（J. Math. Anal. Appl., 2020, 490）.

关键词： L₂^f harmonic forms; weighted p-Poincaré inequality; first p spectrum of f-Laplacian; m-Bakry-E'mery Ricci curvature

本文引用格式

周久儒 . 具有加权p-Poincaré不等式的光滑测度空间上的消灭定理[J]. 数学季刊, 2020 , 35(3) : 311 -319 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.006

Abstract

Key words： L₂^f harmonic forms; weighted p-Poincaré inequality; first p spectrum of f-Laplacian; m-Bakry-E'mery Ricci curvature

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract