報告人簡介
邱國寰博士，現(xiàn)任中國科學院數(shù)學與系統(tǒng)科學研究院研究員，2019年獲得中國數(shù)學會鐘家慶獎。2016年博士畢業(yè)于中國科學技術大學。曾在加拿大麥吉爾大學和香港中文大學從事研究工作。主要研究方向為偏微分方程和幾何分析。相關研究論文發(fā)表在Duke Math J.,Amer.J. Math.,Comm.Math.Phys.等國際一流數(shù)學期刊上。
內(nèi)容簡介
We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex cases. In dimension two, we observe that this curvature equation is equivalent to the equation arising in the optimal transportation problem with a "relative heat cost" function, as discussed in Brenier's paper. When 0 < Θ < π/2 (supercritical phase), the equation violates the Ma-Trudinger-Wang condition. So there may be a singular C^{1,a} solution in supercritical case which is different from the special Lagrangian equation. We have also demonstrated that these gradient estimates of these curvature equations hold for all constant phases. It is worth noting that for the special Lagrangian equation, particularly in subcritical phases, the interior gradient estimate remains an open problem. This is joint work with Xingchen Zhou.
