报告名称：Noncompact Lp-Minkowski problems
主办单位：数学与统计学学院
报告专家：刘佳堃
专家所在单位：University of Wollongong, Australia
报告时间：2019年5月13日9：30-10：30
报告地点：数学与统计学学院201报告厅
专家简介：Dr.Jiakun Liu，DECRA Fellow, University of Wollongong. His main research interests are in nonlinear elliptic and parabolic partial differential equations and applications in geometry and optimal transportation. In particular, the regularity theory of Monge-Ampère equations, Hessian equations, and other variational problems. He is also interested in related areas of geometry and physics, including geometry of convex bodies, minimal surfaces, surfaces of prescribed curvatures, and geometric flows.
Awards and Scholarships：
Discovery Early Career Researcher Award (DECRA), ARC, 2014–2016
URC Small Grants Scheme, University of Wollongong, 2013
Simons Postdoctoral Fellowship, Simons Foundation, Princeton University, 2010–2013
报告摘要：In this talk, we introduce a class of noncompact Lp-Minkowski problems, and prove the existence of complete, noncompact convex hypersurfaces whose p-curvature function is prescribed on a domain in the unit sphere. This problem is related to the solvability of Monge-Ampere equations subject to certain boundary conditions depending on the value of p. The special case of p=1 was previously studied by Pogorelov and Chou-Wang. Here, we give some sufficient conditions for the solvability for general p’s. This is a joint work with Yong Huang at Hunan University.
