《北京数学杂志》学术会议5月18日邀请报告——The $L_p$-Minkowski Problem with Supercritical Exponents
报告人:汪徐家 (Australian National University)
时间:2024-05-18 10:30-11:30
地点:镜春园82号甲乙丙楼报告厅
报告摘要:The $L_p$-Minkowski problem is an extension of the classical Minkowski problem. It can be formulated as the Monge-Ampère equation $$\mathrm{det}(D^2 u+uI)=f(x)u^{p-1}\quad\mbox{on}\ S^n.$$ The corresponding functional is related to the Blaschke-Santalo inequality. Accordingly the problem can be divided into the sub-critical case $p>-n-1$, the critical case $p=-n-1$, and the supercritical case $p<-n-1$. There is a wealth of phenomena regarding the existence and multiplicity of solutions. In this talk we will discuss the existence of solutions for $p$ in the super-critical range $p<-n-1$, and the limit shape of solutions as $p\rightarrow-\infty$.