The "sigma_k Yamabe problem" is a fully nonlinear generalization
of the Yamabe problem, in which one attempts to find a conformal
multiple of a given metric to make constant the k-th elementary
symmetric function of the eigenvalues of the Schouten...
In this talk, I will discuss the quadruple junction solutions in
the entire three dimensional space to a vector-valued Allen-Cahn
equation which models multiple phase separation. The solution is
the basic profile of the local structure near a...
Manifolds with geometric structure carry large and useful
families of non-standard “subharmonic” functions. For example, any
almost complex manifold with hermitian metric carries
plurisubharmonic functions. Moreover, it also carries
“Lagrangian...
This talk is based on joint work with YanYan Li and Eduardo
Teixeira. Some geometric problems in conformal geometry lead
naturally to the study of singular solutions to certain PDEs that
describe "canonical" conformal metrics. A good example is
the...
Conditional on the scattering conjecture of the mass-critical
nonlinear Schrodinger equation in spatial dimension one, we show
that there exists a blow-up solution to the mass-critical
generalized Korteweg de Vries equation (gKdV) with the
minimal...
In 2005 Ma, Trudinger and Wang introduced a fourth-order
differential condition which comes close to be necessary and
sufficient for the smoothness of solutions to optimal transport
problems with a given cost function. If the cost function is
the...
