## Critical exponent semilinear elliptic problems on certain metric-measure spaces

#### Rafe MazzeoStanford UniversityMathematics

I will discuss some rather general analogues of the Yamabe problem on a class of singular spaces and prove the existence of solutions subject to a condition on a new local Yamabe invariant'', which captures conformal information about the singular structure of the underlying space. These results take a much more explicit form when the underlying space is a stratified space. This is joint work with Kazuo Akutagawa and Gilles Carron

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