An invitation to duality theory for variational problems
We introduce generalizations of Calabi’s correspondence between minimal surface equations in Euclidean space (a.k.a. Chaplygin’s ideal gas equation) and maximal surface equations in Lorentz-Minkowski space-time (which also appears in Busemann’s work on irrotational flows of compressible fluids).
Type-II singularities of Ricci flow
Abstract: We will discuss recent progress (by the speaker and collaborators) in determining what rates of finite-time singularity formation are possible for either compact or noncompact solutions of Ricci flow, and in constructing degenerate neckpinch solutions with prescribed asymptotic behaviors.
Robustness of Attractors for Reversible Schnackenberg Equations
For a typical autocatalytic reaction-diffusion system, stochastic reversible Schnackenberg equations with multiplicative white noise, the existence of random attractor and its robustness (upper semicontinuity) as the reverse reaction rate converges to zero are proved through sharp uniform estimates showing the pullback uniform dissipative characteristics.