Vanishing theorems on Riemannian manifolds, and geometric applications |
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| Authors: | Stefano Pigola |
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| Institution: | a Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
b Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy |
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| Abstract: | A general Liouville-type result and a corresponding vanishing theorem are proved under minimal regularity assumptions. The latter is then applied to conformal deformations of stable minimal hypersurfaces, to the L2 cohomology of complete manifolds, to harmonic maps under various geometric assumptions, and to the topology of submanifolds of Cartan-Hadamard spaces with controlled extrinsic geometry. |
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| Keywords: | Vanishing and Liouville theorems Harmonic maps Submanifolds Isolation results |
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