1547671870-The_Ricci_Flow__Chow

BUSEMANN FUNCTIONS 309 and notice that the triangle inequality proves for all s 2 so that Cs,Ts =d(a,1(s)) ~d(a(Ts 0 ),1(s)) ( ...

310 B. SOME RESULTS IN COMPARISON GEOMETRY PROOF. We prove both inclusions s;:: and 2 to obtain equality. (s;::) If x E Iffi'°Y• ...

BUSEMANN FUNCTIONS Hence by Lemma B.52, Cs~ n IHI'Ys = n {x E Mn: b'Ys (x) :SO} )'ER(O) 'YER(O) = {x E Mn : b'Y (x) :S s for a ...

312 B. SOME RESULTS IN COMPARISON GEOMETRY PROPOSITION B.64. For any choice of origin 0 E Mn and alls< t, (B.10) Cs= {x E Ct: ...

ESTIMATING INJECTIVITY RADIUS IN POSITIVE CURVATURE 313 Note that a proper j-gon may be regarded as a proper k-gon for any k & ...

314 B. SOME RESULTS IN COMPARISON GEOMETRY the sectional curvature hypothesis implies exp Pi : B ( 0, 7r / VK) ____, Mn is an im ...

NOTES AND COMMENTARY 315 Parallel translate /3 bt ( 0)) to get a unit vector field U along "It, and define Then V is a Jacobi fi ...

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Bibliography [l] Altschuler, Steven; Angenent, Sigurd B.; Giga, Yoshikazu. Mean curvature flow through singularities for surface ...

318 BIBLIOGRAPHY [21) Bryant, Robert. Local existence of gradient Ricci solitons. Preprint. [22] Casson, Andrew; Jungreis, Dougl ...

BIBLIOGRAPHY 319 [45] Gao, L. Zhiyong. Convergence of Riemannian manifolds; Ricci and Ln/^2 -curvature pinching. J. Differential ...

320 BIBLIOGRAPHY [68] Hamilton, Richard S.; Yau, Shing-Tung. The Harnack estimate for the Ricci flow on a surface-revisited. Asi ...

BIBLIOGRAPHY 321 [91] Li, Peter; Yau, Shing Tung. Estimates of eigenvalues of a compact Riemann- ian manifold. Geometry of the L ...

322 BIBLIOGRAPHY [113] Schoen, R.; Yau, S.-T. Lectures on differential geometry. Lecture notes prepared by Wei Yue Ding, Kung Ch ...

Index almost fiat manifold, 17 ancient solution, 28 ancient, 235 ancient Type I essential point, 272 asymptotic analysis of sing ...

324 on the scale of its maximum curvature, 239 gradient Ricci soliton, 22 on a surface, 112 Gromov-Hausdorff limit, 12, 15, 232 ...

Ricci flow, 1 Ricci identities (commutator formulas), 286 Ricci soliton, 22, 128 on a surface, 112 Ricci-De Turck flow, 80 Rosen ...

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Titles in This Series 110 Bennett Chow and Dan Knopf, The Ricci flow: An introduction, 2004 109 Goro Shimura, Arithmetic and ana ...

TITLES IN THIS SERIES 77 Fumio Hiai and Denes Petz, The semicircle law, free random variables and entropy, 2000 76 Frederick P. ...