Vanishing theorems on Riemannian manifolds, and geometric applications

DOI10.1016/j.jfa.2005.05.007zbMath1087.58022OpenAlexW1997114587WikidataQ125620416 ScholiaQ125620416MaRDI QIDQ2583798

Stefano Pigola, Marco Rigoli, Alberto G. Setti

Publication date: 18 January 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.05.007

zbMATH Keywords

minimal hypersurfaceharmonic mapsvanishing theoremsLiouville theoremsconformal deformationcomplete manifoldisolation results

Mathematics Subject Classification ID

Harmonic maps, etc. (58E20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Related Items (32)

Spacelike translating solitons in Lorentzian product spaces: Nonexistence, Calabi–Bernstein type results and examples ⋮ Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications ⋮ On the homotopy class of maps with finite \(p\)-energy into non-positively curved manifolds ⋮ Entire translating graphs in weighted product spaces: rigidity and nonexistence results ⋮ On a classification theorem for self–shrinkers ⋮ On the uniqueness of complete two-sided hypersurfaces immersed in a class of weighted warped products ⋮ New Calabi-Bernstein type results in Lorentzian product spaces with density ⋮ Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms ⋮ Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs ⋮ Liouville-type theorems on the complete gradient shrinking Ricci solitons ⋮ Aspects of mean curvature flow solitons in warped products ⋮ Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds ⋮ Spacelike submanifolds with parallel Gaussian mean curvature vector: rigidity and nonexistence ⋮ Spacelike translating solitons of the mean curvature flow in Lorentzian product spaces with density ⋮ Remarks on non-compact gradient Ricci solitons ⋮ Rigidity results and topology at infinity of translating solitons of the mean curvature flow ⋮ \(L^p\)-Liouville theorems on complete smooth metric measure spaces ⋮ On the geometry of Einstein-type structures ⋮ A finiteness theorem for the space of \(L^{p}\) harmonic sections ⋮ Existence and non-existence results for a logistic-type equation on manifolds ⋮ Submanifolds immersed in a warped product with density ⋮ Constancy of \(p\)-harmonic maps of finite \(q\)-energy into non-positively curved manifolds ⋮ Liouville type theorem about \(p\)-harmonic function and \(p\)-harmonic map with finite \(L^q\)-energy ⋮ \(L^p\) harmonic 1-forms on minimal hypersurfaces with finite index ⋮ Submanifolds immersed in Riemannian spaces endowed with a Killing vector field: nonexistence and rigidity ⋮ Positive solutions to Schrödinger equations and geometric applications ⋮ Exponentially harmonic maps of complete Riemannian manifolds ⋮ Rigidity of complete spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimes ⋮ Weighted Poincaré inequality and the Poisson Equation ⋮ Liouville-type theorems for weighted \(p\)-harmonic 1-forms and weighted \(p\)-harmonic maps ⋮ REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS ⋮ Some characterizations of space-forms

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