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

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

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

School of Mathematical Sciences, Yangzhou University

Received:2020-06-01 Online:2020-09-30 Published:2020-10-22
About author:ZHOU Jiu-ru(1982-), male, native of Taizhou, Jiangsu, a Lecturer of Yangzhou University, Ph.D, engages in dierential geometry.
Supported by:
Partially supported by National Science Foundation of China(11426195,11771377)； Natural Science Foundation of Jiangsu Province(BK20191435)；

Abstract

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

CLC Number:

O186.12
O178

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.

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

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