• 9 am - 9:50 am: Breakfast
• 9:50 am - 10:40 am: Joel Spruck
• 10:40 am - 10:50 am: Coffee
• 10:50 am - 11:40 am: Bo Guan
• 11:40 pm - 12:40 pm: Lunch break
• 12:40 pm - 1:30 pm: Davi Maximo
• 1:30 pm - 1:40 pm: More Coffee
• 1:40 pm - 2:30 pm: Xin Zhou
Download the symposium flyer here.
1. Joel Spruck:
Title: Complete translating solitons to the mean curvature flow in R3 with nonnegative mean curvature
Abstract: We prove that any complete immersed two sided mean convex translating soliton ⌃ ⇢ R3 for the mean curvature flow is con- vex. As a corollary it follows that any entire mean convex graphical translating soliton in R3 is the axisymmetric ?bowl soliton”. We also show that if the mean curvature of ⌃ tends to zero at infinity, then ⌃ can be represented as an entire graph and so is the bowl soliton. Finally we classify all locally strictly convex graphical translating soli- tons defined over strip regions (the only other possibility).This is joint work with Ling Xiao.
2. Bo Guan:
Title: The concavity and subsolution for fully nonlinear elliptic equa- tions
Abstract: In this talk we discuss the roles of concavity and subsolu- tions in the study of fully nonlinear equations, and report some recent discoveries on how to make use of them to derive second order esti- mates for equations on manifolds under a minimal set of assumptions. We shall discuss di↵erent notions of sub solutions on closed manifolds and show the equivalence between some of the definitions for Type I cones (defined by Ca↵arelli, Nirenberg and Spruck).
3. Davi Maximo:
Title: On Morse index estimates for minimal surfaces
Abstract:In this talk we will survey some recent estimates involving the Morse index and the topology of minimal surfaces.
4. Xin Zhou:
Title: Min-max theory for constant mean curvature (CMC) hyper- surfaces
Abstract: In this talk, I will present constructions of closed CMC hypersurfaces using min-max method. In particular, given any closed Riemannian manifold, I will show the existence of closed CMC hyper- surfaces of any prescribed mean curvature. This is a joint work with Jonathan Zhu.