The Yamabe problem on stratified spaces
By K. Akutagawa, G. Carron, Rafe Mazzeo. 2012
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We introduce new invariants of a Riemannian singular space, the local Yamabe and Sobolev constants, and then go on to prove a general version of the Yamabe theorem under that the global Yamabe invariant of the space is strictly less than one or the other of these local invariants. This rests on a small number of structural assumptions about the space and of the behavior of the scalar curvature function on its smooth locus. The second half of this paper shows how this result applies in the category of smoothly stratified pseudomanifolds, and we also prove sharp regularity for the solutions on these spaces. This sharpens and generalizes the results of Akutagawa and Botvinnik (GAFA 13:259–333, 2003) on the Yamabe problem on spaces with isolated conic singularities.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/2d345594a0650982bfbb630272f88cf4ec2e5a1f
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Citations in the corpus
- Kahler-Einstein metrics with edge singularities (2011, unknown): “Ms,t(φ) := log ωn φ ωn − tfω + sφ, (s, t) ∈ A = (−∞, 0]× [0, 1] ∪ [0, μ]× {1}.”
- On static three-manifolds with positive scalar curvature (2015, methodology): “Accordingly to [1], Sl(N , h) = Wl(N , [h]) > 0, see Lemma 1.”