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We study the isoperimetric problem for the radially symmetric measures.
Weil A., Sur les surfaces a courbure negative, C.R. Acad. Sci. Paris 182 (1926),1069-1071
1926
Earlier work this paper cites.
1938
Earlier work this paper cites.
Almgren F.J., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, 81(1), (1975), 151–154
1975
Earlier work this paper cites.
Borell C., The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30(2), (1975), 207–216
1975
Earlier work this paper cites.
Sudakov V.N., Tsirel’son B.S., Extremal properties of half-spaces for spherically invariant measures, Zap. Nauchn. Otdel. Mat. Inst. Steklov. (LOMI) 41(165), (1974), 14–24, — Problems in the theory of probability distributions, II. Engl. transl. in J. Soviet. Math. 9(1), (1978), 9–17
1978
Earlier work this paper cites.
Erhard A., Symétrisation dans l’espace de Gauss, Math. Scand. 53 (1982), 281–301
1982
Earlier work this paper cites.
Croke C., A sharp four-dimensional isoperimetric inequality, Comment. Math. Helv. 59 (1984), n. 2, 187-192
1984
Earlier work this paper cites.
Borell C., The Ornstein-Uhlenbeck velocity process in backward time and isoperimetry. Chambers University of Technology, 1986-03/ISSN 0347-2809 (preprint)
1986
Earlier work this paper cites.
Kleiner B., An isoperimetric comparison theorem, Invent. Math. 108 (1992), n. 1, 37-47
1992
Earlier work this paper cites.
Some connections between isoperimetric and Sobolev-type inequalities,
Bobkov S.G., Houdre C., · 1997
Earlier work this paper cites.
McCann R.J., A convexity principle for interacting gases, Adv. Math., 128(1), 153–179, 1997
1997
Earlier work this paper cites.
Cordero-Erausquin D., Inégalité de Prékopa-Leindler sur la sphère, CRAS Paris Sèr. I, 329 (1999), 789–792
1999
Cited alongside, same era.
Ambrosio L, Fusco N., Pallara D., Functions of bounded variation, Oxford University Press, 2000
2000
Cited alongside, same era.
Barthe F., Maurey B., Some remarks on isoperimetry of Gaussian type, Ann. Inst. H. Poincaré Probab. Statist., 36 (2000), 419–434
2000
Cited alongside, same era.
Caffarelli L.A., Monotonicity properties of optimal transportation and the FKG and related inequalities, Comm. Math. Phys., 214(3), (2000), 547–563
2000
Cited alongside, same era.
Cordero-Erausquin D., Inégalité géometriqués, Thèse de Doctorat de Mathématiques, Université de Marne-la-Vallée, 2000
2000
Cited alongside, same era.
Morgan F., Manifolds with density, Notices Amer. Math. Soc., 52 (2005), 853-858
2005
Later among the works it cites.
Ritoré M., Optimal isoperimetric inequalities for three-dimensional Cartan-Hadamard manifolds, Global theory of minimal surfaces, 395–404, Clay Math. Proc., 2, Amer. Math. Soc., Providence, RI, 2005
2005
Later among the works it cites.
Rosales C., Cañete A., Bayle V., Morgan F., On the isoperimetric problem in Euclidean space with density, Calc. Var. PDE 31: (2007), 27–46
2007
Later among the works it cites.
Valdimarsson S. I., On the Hessian of optimal transport potential, Ann. Sc. Norm. Sup. Pisa Cl Sci. (5), 6(3) (2007), 441-456
2007
Later among the works it cites.
Barthe F., Kolesnikov A.V., Mass transport and variants of the logarithmic Sobolev inequality, Journal. Geom. Analysis, 18(4), (2008), 921–979
2008
Later among the works it cites.
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Barthe F., Extremal properties of central half-spaces for product measures, J. Func. Anal., 182 (2001), 81–107
2001
Cited alongside, same era.
Ros A., The isoperimetric problem. Lecture at Clay Mathematical Institute on the Global Theory of Minimal Surfaces, summer 2001
2001
Cited alongside, same era.
Gromov M., Isoperimetry of waists and concentrartion of maps, Geom. Anal. Func., 13 (2003), 178–215
2003
Cited alongside, same era.
Morgan F., Regularity of isoperimetric hypersurfaces in Riemennian manifolds, Transactions of Amer. Math. Soc., 335(12) (2003), 5041–5052
2003
Cited alongside, same era.
Bakry D., Ledoux M., Lévy-Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator, Invent. Math., 123(1), (2005), 259–281
2005
Cited alongside, same era.
Cited in the paper.
Huet N., Isoperimetry for spherically symmetric log-concave probability measures (preprint)
Cited in the paper.
Carroll C., Jacob A., Quinn C., Walters R., The isoperimetric problem on planes with density. Bull. of the Australian Math. Soc., 78 (2008), 177–197
2008
Later among the works it cites.
Schulze F., Nonlinear evolution by mean curvature and isoperimetric inequalities, J. Differ. Geom. 79 (2008), 197–241
2008
Later among the works it cites.
Engelstein M., Marcuccio A., Maurmann Q., Pritchard T., Isoperimetric problems on the sphere and on surfaces with density. New York Jour. of Math., 15 (2009), 97–123
2009
Later among the works it cites.
Maurmann Q., Morgan F., Isoperimetric Comparison Theorems for Manifolds with Density, Calculus of variation and partial differential equations, vol. 36(1) (2009), 1–5
2009
Later among the works it cites.
Dahlberg J., Dubbs A., Newkirk E., Tran H., Isoperimetric regions in the plane with density r p r^{p} , New York J. Math. 16 (2010) 31-51
2010
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