In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequence...In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019).展开更多
In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of...In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.展开更多
基金partly supported by the National Natural Science Foundation of China(12061006)the Science and Technology Project of Education Department of Jiangxi Province(GJJ180414)+1 种基金East China University of Technology Research Foundation for Advanced Talents(DHBK2018050)The second author is supported by the National Natural Science Foundation of China(71762001)。
文摘In this paper,we demonstrate the existence part of the discrete Orlicz-Minkowski problem for p-capacity when 1<p<2.
基金supported by National Natural Science Foundation of China(Grant No.11871406)。
文摘In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019).
基金Supported by NSFC(Grant Nos.11271013,61273074,61201065,61203219,11471104)the Fundamental Research Funds for the Central Universities,HUST(Grant Nos.2012QN028 and 2014TS066)+2 种基金IRTSTHN(Grant No.14IRSTHN023)Ph D research startup foundation of He’nan Normal University(Grant No.5101019170120)Youth Science Foundation of He’nan Normal University(Grant No.5101019279032)
文摘In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.
