1547845439-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_I__Chow_

THE CROSS CURVATURE FLOW where we used gtμijk = -Cμijk. By (B.29), μijmμk£nCjR. = 1μijmμjpqμk£nμ£rs EprEqs Hence = 1 (-gipgmq ...

498 B. OTHER ASPECTS OF RICCI FLOW AND RELATED FLOWS PROOF. We compute using the evolution equation for Eij that :t JM (detEt" d ...

THE CROSS CURVATURE FLOW Since this decomposition is orthogonal with respect to E-^1 , we have (B.42) lrijk -Tjik,2 = juijk - ...

500 B. OTHER ASPECTS OF RICCI FLOW AND RELATED FLOWS that (B.45) We have the following nonexistence result. LEMMA B.27 (XCF brea ...

APPENDIX C Glossary adjoint heat equation. When associated to the Ricci flow, the equa- tion is au at + iJ..u - Ru = 0. For a fi ...

502 C. GLOSSARY a solution of the Ricci fl.ow, if !Rm (t) lg(t) :S K on a time interval [O, T) of length on the order of K-^1 , ...

C. GLOSSARY 503 Cartan structure equations. Given an orthonormal frame { ei} and dual coframe { wj}, they are the identities sat ...

504 0. GLOSSARY cosmological constant. A constant c introduced into the Ricci flow equation: a at9ij = -2 (Rij + C9ij). The case ...

C. GLOSSARY 505 eternal solution. A solution of the Ricci flow existing on the time interval ( -oo, oo). Note that eternal solut ...

506 C. GLOSSARY for solutions on closed surfaces and Type I singular solutions on closed 3- manifolds. Jacobi field. A variation ...

C. GLOSSARY 507 little loop conjecture. Hamilton's conjecture which is essentially equivalent to Perelman's no local collapsing ...

508 C. GLOSSARY monotonicity formula. Any formula which implies the monotonicity of a pointwise or integral quantity under a geo ...

C. GLOSSARY 509 Poincare conjecture. The conjecture that any simply-connected closed 3-manifold is diffeomorphic to the 3-sphere ...

510 C. GLOSSARY fields. Formally it is defined by Rm (X, Y) Z ~ Y'x\i'yZ - \7y\7xZ - Y'[x,Y]Z. Rosenau solution. An explicit rot ...

GLOSSARY 511 steady gradient Ricci soliton. A gradient Ricci soliton which is evolving by the pull-back by diffeomorphisms onl ...

512 C. GLOSSARY geometric quantity. For example, given a variation of a metric, we have variation formulas for the Christoffel s ...

Bibliography [1] Alexander, J.W. On the subdivision of 3-space by a polyhedron. Proc. Nat. Acad. Seci, USA, 10, 6-8, 1924. [2] A ...

514 BIBLIOGRAPHY [18] Bakry, D.; Emery, Michel. Diffusions hypercontractives. (French) (Hypercontrac- tive diffusions) Seminaire ...

BIBLIOGRAPHY 515 [40] Buser, Peter; Karcher, Hermann. Gromov's almost fiat manifolds. Asterisque, 81. Societe Mathematique de Fr ...

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