[1] Aubin T. Equations differentielles non lineaires et probleme de Yamabe concernant la courbure scalaire. J Math Pures Appl, 1976, 55(9): 269–296
[2] Avilies P, McOwen R C. Conformal deformation to constant negative scalar curvature onnoncompact Riemannian manifolds. J Diffenrential Geom, 1988, 27(2): 225–235
[3] Grosse N. The Yamabe equation on manifolds of bounded geometry. arXiv: 0912.4398v3
[4] Grosse N. The Yamabe equation on complete manifolds with finite volume. arXiv: 1111.2471v1
[5] Hoffman D, Spruck J. Sobolev and isoperimetric inequalities for Riemannian submanifolds. Comm Pure Appl Math, 1974, 27: 715–727
[6] Jin Z R. A counterexample to the Yamabe problem for complete noncompact manifolds//Lecture Notes in Math. Berlin: Springer, 1988, 1306: 93–101
[7] Michael J H, Simon L M. Sobolev and mean-value inequalities on generalized submanifolds of Rn. Comm Pure Appl Math, 1973, 26: 361–379
[8] Schoen R. Conformal deformation of a Riemannian metric to constant scalar curvature. J Diffenrential Geom, 1984, 2: 479–495
[9] Simon L M. Existence of surfaces minimizing the Willmore functional. Comm Anal Geom, 1993, 2: 281–326
[10] Topping P. Mean curvature flow and geometric inequalities. J Reine Angew Math, 1998, 503: 47–61
[11] Topping P. Diameter control under Ricci flow. Comm Anal Geom, 2005, 13: 1039–1055
[12] Topping P. Relating diameter and mean curvature for submanifolds of Euclidean space. Comment Math Helvetici, 2008, 83: 539–546
[13] Wu J Y, Zheng Y. Relating diameter and mean curvature for Riemannian submanifolds. arXiv: 1001.3463v2 |