The Gursky–Streets equations
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DOI: 10.1007/s00208-020-02021-5
Abstract: Gursky–Streets introduced a formal Riemannian metric on the space of conformal metrics in a fixed conformal class of a compact Riemannian four-manifold in the context of the $$\sigma _2$$ σ 2 -Yamabe problem. The geodesic… read more here.
Keywords: regularity; yamabe problem; uniform regularity; gursky streets ... See more keywords
Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry
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DOI: 10.1016/j.aim.2018.07.006
Abstract: We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler-Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the… read more here.
Keywords: invariant surface; surface area; yamabe problem; geometry ... See more keywords
On the existence of extremals for the weighted Yamabe problem on compact manifolds
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DOI: 10.1016/j.difgeo.2019.101585
Abstract: Abstract In [3] , J.S. Case considered a Yamabe type problem in the setting of smooth measure space for a Riemannian manifold and a parameter m, which generalize the original Yamabe problem when m =… read more here.
Keywords: existence extremals; weighted yamabe; yamabe problem; extremals weighted ... See more keywords
On higher-dimensional singularities for the fractional Yamabe problem: A nonlocal Mazzeo–Pacard program
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DOI: 10.1215/00127094-2019-0034
Abstract: We consider the problem of constructing solutions to the fractional Yamabe problem that are singular at a given smooth sub-manifold, and we establish the classical gluing method of Mazzeo and Pacard for the scalar curvature… read more here.
Keywords: fractional yamabe; yamabe problem; mazzeo pacard; geometry ... See more keywords