## Speaker:

Peter Smillie

## Institution:

Caltech

## Time:

Tuesday, January 14, 2020 - 4:00pm

## Location:

RH 306

In joint work with F. Bonsante and A. Seppi, we solve a

Dirichlet-type problem for entire constant mean curvature hypersurfaces in

Minkowski n+1-space, proving that such surfaces are essentially in bijection

with lower semicontinuous functions on the n-1-sphere. This builds off of

existence theorems by Treibergs and Choi-Treibergs, which themselves rely on

the foundational work of Cheng and Yau. I'll present their maximum principle

argument as well the extra tool that leads to our complete existence and

uniqueness theorem. Time permitting, I'll compare with the analogous problem

of constant Gaussian curvature and present a new result on their intrinsic

geometry.