Title: Three theorems about asymptotic expansions of harmonic functions at the boundaryAbstract: Consider a harmonic function on a domain, vanishing along a part of its boundary, and a point on […]
Title: Boundary behavior of the Allen-Cahn equation and the construction of free boundary minimal hypersurfacesAbstract: In the late 70s, the work of Modica, Mortola, De Giorgi, and many others established […]
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 […]
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 […]
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 […]
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 […]
Title: Strichartz estimates for the Schrödinger equation on the sphere. Abstract: We will discuss Strichartz estimates for solutions of the Schrödinger equation on the standard round sphere, which is related to […]
Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a […]
Title: On isolated singularities and generic regularity of min-max CMC hypersurfacesAbstract: Smooth constant mean curvature (CMC) hypersurfaces serve as effective tools to study the geometry and topology of Riemannian manifolds. […]
Tittle: Partial regularity for Lipschitz solutions to the minimal surface system Abstract: The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces […]
Title: The Lawson-Osserman conjecture for the minimal surface systemAbstract: In their seminal work on the minimal surface system, Lawson and Osserman conjectured that Lipschitz graphs that are critical points of […]
Title: The Nevo-Thangavelu spherical maximal function on two step nilpotent Lie groups.Consider R^d times R^m with the group structure of a 2-step Carnot Lie group and natural parabolic dilations. The […]