Yamabe equation on some complete noncompact manifolds

Wei, Guodong

doi:10.2140/pjm.2019.302.717

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2022

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Cited by 2 publications

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“…Finally, to the best of our knowledge, Theorems 1.8, 1.9 and 1.11 are new even in the Euclidean setting. In the more general Riemannian setting, we point out some existence results of variational solutions for the Yamabe equation under conditions on the Yamabe constant and the Yamabe constant at infinity, see [17,24]. We explicitly note that the Yamabe equation reduces to (1.5) when n ≥ 3 and the manifold is scalar flat.…”

Section: (N−4)mentioning

confidence: 97%

Semilinear elliptic equations on manifolds with nonnegative Ricci curvature

Catino¹,

Monticelli²

2022

Preprint

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In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case that all nonnegative solutions vanish identically. Moreover, under some natural assumptions, in the critical case we prove a strong rigidity result, namely we classify all nontrivial solutions showing that they exist only if the potential is constant and the manifold is isometric to the Euclidean space.4 n−2 g, u > 0, is given by

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Section: (N−4)mentioning

confidence: 97%