In this talk,we will survey some of the recent developments on the existence and regularity of free boundary minimal surfaces,including in particular some j
We discuss possible interesting consequences when the material parameters of metamaterials/metasurfaces exhibit wave-vector-dependence,which is also known a
Let $u_n$ be a sequence of mappings from a closed Riemannian surface $M$ to a general Riemannian manifold $NsubsetR^k$.If $u_n$ satisfies sup n(‖(▽)un‖
This is a report on my joint work with Vincent Bonini and Shiguang Ma.Using the so-called horospherical metrics for immersed hypersurfaces with certain conv
S.T.Yau conjectured that the first eigenvalue of every closed minimal hypersurface in the unit sphere is just its dimension.We prove this conjecture for min
We study the minimal surface equation in the hyperbolic space over singular domains.Under appropriate assumptions on the domains,we prove the existence of s
We survey some new and old,positive and negative results on a priori estimates,regularity,and rigidity for special Lagrangian equations with or without cert