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  Isotropic Curvature and the Ricci Flow

Nguyen, H. T. (2010). Isotropic Curvature and the Ricci Flow. International Mathematics Research Notices, 2010(3): rnp147, pp. 536-558. doi:10.1093/imrn/rnp147.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-9DDC-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-9DDF-3
Genre: Journal Article

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 Creators:
Nguyen, Huy T.1, Author              
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1Geometric Analysis and Gravitation, AEI Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              

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 Abstract: In this paper, we study the Ricci flow on higher dimensional compact manifolds. We prove that nonnegative isotropic curvature is preserved by the Ricci flow in dimensions greater than or equal to four. In order to do so, we introduce a new technique to prove that curvature functions defined on the orthonormal frame bundle are preserved by the Ricci flow. At a minimum of such a function, we compute the first and second derivatives in the frame bundle. Using an algebraic construction, we can use these expressions to show that the nonlinearity is positive at a minimum. Finally, using the maximum principle, we can show that the Ricci flow preserves the cone of curvature operators with nonnegative isotropic curvature.

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 Dates: 2010-05-052009-092010
 Publication Status: Published in print
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 Identifiers: DOI: 10.1093/imrn/rnp147
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Title: International Mathematics Research Notices
Source Genre: Journal
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Pages: - Volume / Issue: 2010 (3) Sequence Number: rnp147 Start / End Page: 536 - 558 Identifier: -