陈正茂博士学术报告：Some Lp Minkowski problems for weighted measures

报告人：陈正茂博士

报告标题：Some Lp Minkowski problems for weighted measures

报告时间：2022年6月17日（星期五）15:30-16:30

报告地点：育才校区数学楼304

腾讯会议： 868-976-977

报告摘要：Motivated by the great works of Huang, Xi and Zhao (Adv. Math. 385 (2021), https://doi.org/10.1016/j.aim.2021.107769 ) and Cordero-Erausquin and Klartag (J. Funct. Anal. 268 (2015), 3834-3866), we define the so-called Lp surface area measure for weighted measures. In an unified framework, we introduce some geometric measures arisen in Convex Geometry and Potential Theory, such as the classical surface area measure, curvature measure, dual curvature measure, harmonic measure, capacity measure, torsional rigidity measure, the first eigenvalue measure of elliptic operators. Under suitable conditions, the Lp surface area measure for weighted measures mentioned above is absolutely continuous with respect to the surface measure and is weakly continuous in the sense of Hausdorff metric when considering it as a functional of domain. Some Lp Minkowski problems for weighted measures were posed and solved.

报告人简介：陈正茂，男，博士。2020年6月博士毕业于湖南师范大学，目前在广州大学从事博士后研究工作，主要从事非线性偏微分方程与几何分析方面的研究，如由非线性椭圆方程导出的Minkowski问题等，研究成果发表在Calc. Var. Partial Differential Equations，Proc. Roy. Soc. Edinburgh Sect. A, Potential Anal. 等SCI期刊。