Krylov-Evans type theorem for twisted Monge-Amp\'ere equations

Friday, September 25, 2015 -
3:00pm to 4:00pm
Motivated by the pluriclosed flow of Streets and Tian, we establish Evans-Krylov type estimates for parabolic "twisted" Monge-Ampere equations in both the real and complex setting. In particular, a bound on the second derivatives on solutions to these equations yields bounds on Holder norms of the second derivatives. These equations are parabolic but neither not convex nor concave, so the celebrated proof of Evans-Krylov does not apply. In the real case, the method exploits a partial Legendre transform to form second derivative quantities which are subsolutions. Despite the lack of a bona fide complex Legendre transform, we show the result holds in the complex case as well, by formally aping the calculation. This is joint work with Jeff Streets. 
Speaker: 
Micah Warren
University of Oregon
Event Location: 
Fine Hall 314