Tianyuan Mathematical Center
in Southwest China

Exterior Bernstein and Bernstein problems for Hessian equations

[Math. Dept.]

July 06, 2018  11:30-12:30

E409  School of Mathematics

SPEAKER

Yuan Yu (University of Washington)

ABSTRCT

We survey some new and old uniqueness results for Hessian equations such as special Lagrangian equations, Monge-Ampere equations, and symmetric Hessian equations. In particular, a unified approach to quadratic asymptote of solutions over exterior domains--based on an "exterior" Evans-Krylov, corresponding to Allard-Almgren's uniqueness of tangent cones in minimal surface situation--will be presented (joint with D.S. Li and Zh.S. Li). Special Lagrangian and Monge-Ampere equations are the potential equations for minimal and maximal "gradient" graphs in Euclid and pseudo-Euclid spaces respectively.

SUPPORTED BY

Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University