Nonlinear problems in geometry

OCT 19, 2017 | 9:00 AM TO 2:30 PM



The Graduate Center
365 Fifth Avenue


4102: Science Center


October 19, 2017: 9:00 AM-2:30 PM




Initiative for the Theoretical Sciences



• 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.