Geometry & Topology Volume 19, issue 3 (2015)

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ISSN (electronic): 1364-0380

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Slowly converging Yamabe flows

Alessandro Carlotto, Otis Chodosh and Yanir A Rubinstein

Geometry & Topology 19 (2015) 1523–1568

DOI: 10.2140/gt.2015.19.1523

Bibliography

1	D Adams, L Simon, Rates of asymptotic convergence near isolated singularities of geometric extrema, Indiana Univ. Math. J. 37 (1988) 225 MR963501
2	T Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 (1976) 269 MR0431287
3	M Berger, P Gauduchon, E Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Mathematics 194, Springer (1971) MR0282313
4	J Bergh, J Löfström, Interpolation spaces: An introduction, Grundl. Math. Wissen. 223, Springer (1976) MR0482275
5	R G Bettiol, P Piccione, Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions, Pacific J. Math. 266 (2013) 1 MR3105774
6	M F Bidaut-Véron, M Bouhar, On characterization of solutions of some nonlinear differential equations and applications, SIAM J. Math. Anal. 25 (1994) 859 MR1271314
7	S Brendle, Convergence of the Yamabe flow for arbitrary initial energy, J. Differential Geom. 69 (2005) 217 MR2168505
8	S Brendle, Convergence of the Yamabe flow in dimension $6$ and higher, Invent. Math. 170 (2007) 541 MR2357502
9	S Brendle, A short proof for the convergence of the Yamabe flow on $S^n$, Pure Appl. Math. Q. 3 (2007) 499 MR2340052
10	S Brendle, Evolution equations in Riemannian geometry, Jpn. J. Math. 6 (2011) 45 MR2835361
11	L A Caffarelli, B Gidas, J Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271 MR982351
12	R Chill, On the \Lojasiewicz–Simon gradient inequality, J. Funct. Anal. 201 (2003) 572 MR1986700
13	R Chouikha, F B Weissler, Monotonicity properties of the period function and the number of constant scalar curvature metrics on $S^1\times S^{n-1}$, preprint (1994)
14	B Chow, The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature, Comm. Pure Appl. Math. 45 (1992) 1003 MR1168117
15	B Clarke, Y A Rubinstein, Ricci flow and the metric completion of the space of Kähler metrics, Amer. J. Math. 135 (2013) 1477 MR3145001
16	B Gidas, W M Ni, L Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209 MR544879
17	K Kröncke, Ricci flow, Einstein metrics and the Yamabe invariant, arXiv:1312.2224
18	J M Lee, T H Parker, The Yamabe problem, Bull. Amer. Math. Soc. 17 (1987) 37 MR888880
19	G M Lieberman, Second order parabolic differential equations, World Scientific (1996) MR1465184
20	S Łojasiewicz, Une propriété topologique des sous-ensembles analytiques réels, from: "Les Équations aux Dérivées Partielles", Éditions du CNRS (1963) 87 MR0160856
21	R Mazzeo, D Pollack, K Uhlenbeck, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc. 9 (1996) 303 MR1356375
22	P Petersen, Riemannian geometry, Graduate Texts in Mathematics 171, Springer (2006) MR2243772
23	Y A Rubinstein, Smooth and singular Kähler–Einstein metrics, from: "Geometric and Spectral Analysis" (editors P Albin, D Jakobson, F Rochon), Contemp. Math. 630, Amer. Math. Soc. and Centre Recherches Mathematiques (2014) 45
24	R M Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984) 479 MR788292
25	R M Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, from: "Topics in calculus of variations" (editor M Giaquinta), Lecture Notes in Math. 1365, Springer (1989) 120 MR994021
26	H Schwetlick, M Struwe, Convergence of the Yamabe flow for “large” energies, J. Reine Angew. Math. 562 (2003) 59 MR2011332
27	L Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. 118 (1983) 525 MR727703
28	L Simon, Theorems on regularity and singularity of energy minimizing maps, Birkhäuser (1996) MR1399562
29	M Struwe, Curvature flows on surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. 1 (2002) 247 MR1991140
30	N S Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968) 265 MR0240748
31	H Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960) 21 MR0125546
32	R Ye, Global existence and convergence of Yamabe flow, J. Differential Geom. 39 (1994) 35 MR1258912
33	E Zeidler, Nonlinear functional analysis and its applications, I: Fixed-point theorems, Springer (1986) MR816732