Integral Ricci curvature bounds along geodesics for nonexpanding gradient Ricci solitons |
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Authors: | Bennett Chow Peng Lu Bo Yang |
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Institution: | 1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA 2. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA
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Abstract: | Following Li and Yau (Acta Math 156:153?C201 1986) and similar to Perelman (The entropy formula for the Ricci flow and its geometric applications), we define an energy functional ${\mathcal{J}}$ associated to a smooth function ${\phi}$ on a complete Riemannian manifold. As an application, we deduce integral Ricci curvature upper bounds along modified geodesics for complete steady and shrinking gradient Ricci solitons. |
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