In this paper, we prove a reverse Hölder inequality for the eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with the integral Ricci curvature condition. We also prove an isoperimetric inequality for the torsional rigidity of such domains. These results extend some recent work of Gamara et al. (Open Math. 13(1), 557–570, 2015) and Colladay et al. (J. Geom. Anal. 28(4), 3906–3927, 2018) from the pointwise lower Ricci curvature bound to the integral Ricci curvature condition. We also extend the results from Laplacian to p-Laplacian.

中文翻译：

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积分Ricci曲率条件下的Chiti型逆Hölder不等式和扭转刚度

在本文中，我们证明了在具有积分Ricci曲率条件的紧致黎曼流形域上Dirichlet问题的本征函数的逆Hölder不等式。我们还证明了此类区域的扭转刚度的等距不等式。这些结果扩展了Gamara等人的最新工作。（开放数学式13（1），557-570，2015）和Colladay等。（J.的Geom。元素分析28从逐点（4），3906-3927，2018）降低结合到积分Ricci曲率条件Ricci曲率。我们还将结果从拉普拉斯算子扩展到p-拉普拉斯算子。