Abstract:

In this talk we will discuss the problem of finding a locally convexhypersurface S in R^{n+1}

of constant curvature f(\kappa)=\sigma>0 with prescribed boundary \Gamma. Here f is a smooth

symmetric function and \kappa=(\kappa_1, ... , \kappa_n) are the principal curvatures of S.

The function f(\kappa) must satisfy additional conditions so that theresulting fully nonlinear equation

for S is elliptic. A classical example is f(\kappa)=\sigma_n(\kappa)=K the (extrinsic) Gauss curvature.

This question is quite subtle for even deciding when a smooth Jordancurve in R^3 bounds a surface

of positive curvature is open.

In this talk we will discuss the problem of finding a locally convexhypersurface S in R^{n+1}

of constant curvature f(\kappa)=\sigma>0 with prescribed boundary \Gamma. Here f is a smooth

symmetric function and \kappa=(\kappa_1, ... , \kappa_n) are the principal curvatures of S.

The function f(\kappa) must satisfy additional conditions so that theresulting fully nonlinear equation

for S is elliptic. A classical example is f(\kappa)=\sigma_n(\kappa)=K the (extrinsic) Gauss curvature.

This question is quite subtle for even deciding when a smooth Jordancurve in R^3 bounds a surface

of positive curvature is open.

February 6th, Wednesday, 5:00-6:00 pm

Mathematics
520

Tea
will be served at 4:30pm