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

ZHOU Jiu-ru

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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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)；

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Abstract

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）.

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

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ZHOU Jiu-ru . Vanishing Theorems on Smooth Metric Measure Spaces with a Weighted p-Poincaré Inequality[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(3) : 311 -319 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.006

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