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arXiv · 1306.4373

The Yamabe problem on Dirichlet spaces

Kazuo Akutagawa·Gilles Carron·Rafe Mazzeo
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Abstract

We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces furnishing the key examples. The criterion for solvability there is phrased in terms of a strict inequality of the global Yamabe invariant with a `local Yamabe invariant', which captures information about the local singular structure. All of this is generalized here to the setting of Dirichlet spaces which admit a Sobolev inequality and satisfy a few other mild hypotheses. Applications include a new approach to the nonspherical part of the CR Yamabe problem.

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Kazuo Akutagawa, Gilles Carron, Rafe Mazzeo. 2013-06-18. The Yamabe problem on Dirichlet spaces. https://arxiv.org/abs/1306.4373

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