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The weighted
$\sigma_k$-curvature of a smooth metric measure space
Jeffrey S. Case |
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Vol. 299 (2019), No. 2, 339–399
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DOI: 10.2140/pjm.2019.299.339
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Abstract |
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We propose a definition of the weighted -curvature of a smooth metric measure space and justify it in two ways. First, we show that the weighted -curvature prescription problem is governed by a fully nonlinear second order elliptic PDE which is variational when or the smooth metric measure space is locally conformally flat in the weighted sense. Second, we show that, in the variational cases, quasi-Einstein metrics are stable with respect to the total weighted -curvature functional. We also discuss related conjectures for weighted Einstein manifolds. |
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Keywords
smooth metric measure space, $\sigma_k$-curvature,
quasi-Einstein, weighted Einstein
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Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 35J60, 58E11
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Milestones
Received: 12 January 2017
Revised: 3 June 2018
Accepted: 7 October 2018
Published: 21 May 2019
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Authors |
| Jeffrey S. Case | |
| Mathematics Department Penn State University University Park, PA United States |
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