Harmonic Functions on Manifolds with Nonnegative Ricci Curvature and Linear Volume Growth

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dc.creatorSormani, Christina
dc.date1999-03-29
dc.date.accessioned2026-07-07T05:28:32Z
dc.date.available2026-07-07T05:28:32Z
dc.descriptionLower bounds on Ricci curvature limit the volumes of sets and the existence of harmonic functions on Riemannian manifolds. In 1975, Shing Tung Yau proved that a complete noncompact manifold with nonnegative Ricci curvature has no nonconstant harmonic functions of sublinear growth. In the same paper, Yau used this result to prove that a complete noncompact manifold with nonnegative Ricci curvature has at least linear volume growth. In this paper, we prove the following theorem concerning harmonic functions on these manifolds. Theorem: Let M be a complete noncompact manifold with nonnegative Ricci curvature and at most linear volume growth. If there exists a nonconstant harmonic function, f, of polynomial growth of any given degree q, then the manifold splits isometrically, M= N x R.
dc.descriptionTo appear in Pacific Journal of Mathematics, submitted April 1998, 7pp
dc.identifierhttps://arxiv.org/abs/math/9903172
dc.identifierhttp://arxiv.org/abs/math/9903172
dc.identifierPacific Journal of Mathematics, Vol 192, No. 1, pp 183-189, January 2000.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78290
dc.subjectDifferential Geometry
dc.subject53C20; 31C05
dc.titleHarmonic Functions on Manifolds with Nonnegative Ricci Curvature and Linear Volume Growth
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