Title: Soap films, Plateau's laws, and the Allen-Cahn equation Abstract: Plateau's problem of minimizing area among surfaces with a common boundary is the basic model for soap films and leads to the theory of minimal surfaces. In this talk we will discuss a modification of Plateau's problem in which surfaces are replaced with regions of small […]
Title: First eigenvalue estimates on asymptotically hyperbolic manifolds and their submanifolds.  Abstract: I will report on joint work with Samuel Pérez-Ayala. We derive a sharp upper bound for the first eigenvalue $lambda_{1,p}$ of the $p$-Laplacian on asymptotically hyperbolic manifolds for $1<p<infty$. We then prove that a particular class of conformally compact submanifolds within asymptotically hyperbolic […]
Title: Recovery of time-dependent coefficients in hyperbolic equations on Riemannian manifolds from partial data.Abstract: In this talk we discuss inverse problems of determining time-dependent coefficients appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in […]
Title: A family of Kahler flying wing steady Ricci solitonsAbstract: Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.-D. Cao in complex dimension n>2. This is joint […]