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Talks by Rafe Mazzeo

Asymptotics of special metrics

Stanford University

I will discuss some recent results concerning the existence and nature of asymptotic expansions for various classes of metrics with special geometry. The focus will be on explaining how these asymptotic expansions are useful for existence questions for these metrics, or for understanding certain global (spectral or geometric) invariants of these spaces.

The Yamabe Problem on Stratified Spaces

Stanford University

I will discuss recent work with Akutagawa and Carron concerning the solvability of the Yamabe problem to compact stratified spaces. There are many new obstructions to solvability, some of which we identify quite explicitly. We also discuss regularity of the solutions along the singular strata, and identify some possible rigidity phenomena for cases where existence fails.

Boundary regularity and the renormalized area functional

Stanford University

In previous joint work with Alexakis, we studied the renormalized area of properly embedded minimal surfaces in hyperbolic space, which turns out to be closely related to Willmore energy. In new work, we obtain some results about how control of this renormalized area of a minimal surface leads to some regularity of its asymptotic boundary.
Esta conferencia se enmarca dentro del convenio de colaboración entre las universidades de Granada y Stanford y forma parte de la acción integrada Granada-Stanford
Seminario de conferencias del doctorado interuniversitario Matemáticas

Aula A12, Facultad de Ciencias

Rafe Mazzeo

Stanford University

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