ABP estimate and geometric inequalities

作者：Xia, Chao^*; Zhang, Xiangwen

来源：Communications in Analysis and Geometry, 2017, 25(3): 685-708.

DOI：10.4310/CAG.2017.v25.n3.a6

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In this paper, we present the proofs for several geometric inequalities using the Alexandrov-Bakelman-Pucci (ABP) estimate on Riemannian manifolds. First, we give new proofs of the HeintzeKarcher inequality for mean convex domain on manifolds with nonnegative Ricci curvature and the classical Minkowski inequality for mixed volumes. Then, we prove the anisotropic Heintze-Karcher inequality. Along the new approach, we also establish an anisotropic version of ABP estimate which may be of independent interest.

• 出版日期2017
• 单位厦门大学