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Volumn 62, Issue 1, 2002, Pages 17-38

Sharp affine LP sobolev inequalities

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EID: 0038381937     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1090425527     Document Type: Article
Times cited : (355)

References (42)
  • 1
    • 0003255464 scopus 로고
    • Nonlinear Analysis on Manifolds: Monge-Ampere Equations
    • Springer-Verlag, Berlin
    • T. Aubin, Nonlinear Analysis on Manifolds: Monge-Ampere Equations, Grundlehren der Mathematischen Wissenschaften, 252, Springer-Verlag, Berlin, 1982.
    • (1982) Grundlehren Der Mathematischen Wissenschaften , vol.252
    • Aubin, T.1
  • 2
    • 84972498579 scopus 로고
    • Problemes isoperimetriques et espaces de Sobolev
    • T. Aubin, Problemes isoperimetriques et espaces de Sobolev, J. Differential Geom. 11 (1976) 573-598.
    • (1976) J. Differential Geom , vol.11 , pp. 573-598
    • Aubin, T.1
  • 3
    • 0033114779 scopus 로고    scopus 로고
    • On the best Sobolev inequality
    • T. Aubin & Y.Y. Li, On the best Sobolev inequality, J. Math. Pure Appl. 78 (1999) 353-387.
    • (1999) J. Math. Pure Appl , vol.78 , pp. 353-387
    • Aubin, T.1    Li, Y.Y.2
  • 4
    • 84963015788 scopus 로고
    • An integral inequality
    • G.A. Bliss, An integral inequality, J. London Math. Soc. 5 (1930) 40-46.
    • (1930) J. London Math. Soc , vol.5 , pp. 40-46
    • Bliss, G.A.1
  • 5
    • 0030533361 scopus 로고    scopus 로고
    • Levy-Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator
    • D. Bakry & M. Ledoux, Levy-Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator, Invent. Math. 123 (1996) 259-281.
    • (1996) Invent. Math , vol.123 , pp. 259-281
    • Bakry, D.1    Ledoux, M.2
  • 6
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Annals Math. 138 (1993) 213-242.
    • (1993) Annals Math , vol.138 , pp. 213-242
    • Beckner, W.1
  • 7
    • 0031987054 scopus 로고    scopus 로고
    • On sharp Sobolev embedding and the logarithmic Sobolev inequality
    • W. Beckner & M. Pearson, On sharp Sobolev embedding and the logarithmic Sobolev inequality, Bull. Lond. Math. Soc. 30 (1998) 80-84.
    • (1998) Bull. Lond. Math. Soc , vol.30 , pp. 80-84
    • Beckner, W.1    Pearson, M.2
  • 8
    • 0031232439 scopus 로고    scopus 로고
    • Some connections between isoperimetric and Sobolev-type inequalities
    • S. Bobkov & C. Houdre, Some connections between isoperimetric and Sobolev-type inequalities, Memoirs of Amer. Math. Soc., 616, 1997.
    • (1997) Memoirs of Amer. Math. Soc. , pp. 616
    • Bobkov, S.1    Houdre, C.2
  • 9
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • H. Brezis & L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477.
    • (1983) Comm. Pure Appl. Math , vol.36 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 11
    • 0037091874 scopus 로고    scopus 로고
    • The Lp-Buseman-Petty centroid inequality
    • S. Campi & P. Gronchi, The Lp-Buseman-Petty centroid inequality, Adv. Math. 167(1) (2002) 128-141.
    • (2002) Adv. Math , vol.167 , Issue.1 , pp. 128-141
    • Campi, S.1    Gronchi, P.2
  • 12
    • 38249020884 scopus 로고
    • Extremals of functionals with competing symmetry
    • E. Carlen & M. Loss, Extremals of functionals with competing symmetry J. Funct. Anal. 88 (1990) 437-456.
    • (1990) J. Funct. Anal , vol.88 , pp. 437-456
    • Carlen, E.1    Loss, M.2
  • 13
    • 0001611867 scopus 로고
    • On the existence of an extremal function for an inequality of J. Moser
    • L. Carleson & S.Y.A. Chang, On the existence of an extremal function for an inequality of J. Moser, Bull. Sci. Math. 110 (1986) 113-127.
    • (1986) Bull. Sci. Math , vol.110 , pp. 113-127
    • Carleson, L.1    Chang, S.Y.A.2
  • 14
    • 2442569048 scopus 로고    scopus 로고
    • The Moser-Trudinger inequality and applications to some problems in conformal geometry
    • Park City, UT, 1992, IAS/Park City Math. Ser., 2, Amer. Math. Soc., Providence, RI
    • S.Y.A. Chang, The Moser-Trudinger inequality and applications to some problems in conformal geometry, Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), 65-125, IAS/Park City Math. Ser., 2, Amer. Math. Soc., Providence, RI, 1996.
    • (1996) Nonlinear Partial Differential Equations in Differential Geometry , pp. 65-125
    • Chang, S.Y.A.1
  • 16
    • 0001216371 scopus 로고    scopus 로고
    • Optimal Sobolev inequalities of arbitrary order on Riemannian compact manifolds
    • O. Druet, Optimal Sobolev inequalities of arbitrary order on Riemannian compact manifolds, J. Funct. Anal. 159 (1998) 217-242.
    • (1998) J. Funct. Anal , vol.159 , pp. 217-242
    • Druet, O.1
  • 18
    • 0000562793 scopus 로고
    • Normal and, integral currents
    • H. Federer & W. Fleming, Normal and, integral currents, Ann. Math. 72 (1960) 458-520.
    • (1960) Ann. Math , vol.72 , pp. 458-520
    • Federer, H.1    Fleming, W.2
  • 20
    • 0009389702 scopus 로고
    • Isoperimetric inequalities in Riemannian manifolds
    • (by V.D. Milman and G. Schecht-man), Lect. Notes in Math, Springer-Verlag, Berlin
    • M. Gromov, Isoperimetric inequalities in Riemannian manifolds, in ‘Asymptotic Theory of Finite Dimensional Normed Spaces’ (by V.D. Milman and G. Schecht-man), Lect. Notes in Math., 1200, Springer-Verlag, Berlin, 1986.
    • (1986) Asymptotic Theory of Finite Dimensional Normed Spaces , vol.1200
    • Gromov, M.1
  • 21
    • 0038685490 scopus 로고
    • An isoperimetric estimate for the Ricci flow on the two-sphere
    • (Princeton, NJ, 1992), Princeton Univ. Press, Princeton, NJ
    • R. Hamilton, An isoperimetric estimate for the Ricci flow on the two-sphere, in ‘Modern methods in complex analysis’ (Princeton, NJ, 1992), 191-200, Ann. of Math. Stud., 137, Princeton Univ. Press, Princeton, NJ, 1995.
    • (1995) Modern Methods in Complex Analysis , vol.137 , pp. 191-200
    • Hamilton, R.1
  • 22
    • 0003286319 scopus 로고    scopus 로고
    • Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities
    • New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI
    • E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, Courant Lecture Notes in Mathematics, 5, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.5
    • Hebey, E.1
  • 23
    • 84974004186 scopus 로고
    • The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
    • E. Hebey & Vaugon, V, The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Math. J. T9 (1995) 235-279.
    • (1995) Duke Math. J , vol.T9 , pp. 235-279
    • Hebey, E.1    Vaugon, V.2
  • 24
    • 0038685489 scopus 로고
    • A Sobolev inequality for Riemannian submanifolds
    • Proc. Sympos. Pure Math., Vol, Stanford Univ., Stanford, Calif., 1973, Amer. Math. Soc., Providence, R.I
    • D. Hoffman & J. Spruck, A Sobolev inequality for Riemannian submanifolds, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 1, 139-141. Amer. Math. Soc., Providence, R.I., 1975.
    • (1975) Differential Geometry , vol.27 , pp. 139-141
    • Hoffman, D.1    Spruck, J.2
  • 25
    • 84878385683 scopus 로고    scopus 로고
    • Affine geometry of convex bodies
    • Heidelberg
    • K. Leichtweiss, Affine geometry of convex bodies, Johann Ambrosius Barth, Heidelberg, 1998.
    • (1998) Johann Ambrosius Barth
    • Leichtweiss, K.1
  • 26
    • 0032221698 scopus 로고    scopus 로고
    • Sharp Sobolev inequalities involving boundary terms
    • Y.Y. Li & M. Zhu, Sharp Sobolev inequalities involving boundary terms, Geom. Funct. Anal. S (1998) 59-87.
    • (1998) Geom. Funct. Anal. S , pp. 59-87
    • Li, Y.Y.1    Zhu, M.2
  • 27
    • 0000298073 scopus 로고
    • Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
    • E.H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Annals of Math. 115 (1983) 349-374.
    • (1983) Annals of Math , vol.115 , pp. 349-374
    • Lieb, E.H.1
  • 28
    • 0001874829 scopus 로고
    • On some affine isoperimetric inequalities
    • E. Lutwak, On some affine isoperimetric inequalities, J. Differential Geom. 23 (1986) 1-13.
    • (1986) J. Differential Geom , vol.23 , pp. 1-13
    • Lutwak, E.1
  • 29
    • 84972508818 scopus 로고
    • The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem
    • E. Lutwak, The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem, J. Differential Geom. 38 (1993) 131-150.
    • (1993) J. Differential Geom , vol.38 , pp. 131-150
    • Lutwak, E.1
  • 30
    • 84972497535 scopus 로고
    • On the regularity of solutions to a generalization of the Minkowski problem
    • E. Lutwak & V. Oliker, On the regularity of solutions to a generalization of the Minkowski problem, J. Differential Geom. 41 (1995) 227-246.
    • (1995) J. Differential Geom , vol.41 , pp. 227-246
    • Lutwak, E.1    Oliker, V.2
  • 31
    • 0003157976 scopus 로고    scopus 로고
    • On Lp affine isoperimetric inequalities
    • E. Lutwak, D. Yang & G. Zhang, On Lp affine isoperimetric inequalities, J. Differential Geom. 56 (2000) 111-132.
    • (2000) J. Differential Geom , vol.56 , pp. 111-132
    • Lutwak, E.1    Yang, D.2    Zhang, G.3
  • 33
    • 0031227458 scopus 로고    scopus 로고
    • Blaschke-Santalo inequalities
    • E. Lutwak & G. Zhang, Blaschke-Santalo inequalities, J. Differential Geom. 4T (1997) 1-16.
    • (1997) J. Differential Geom , vol.4T , pp. 1-16
    • Lutwak, E.1    Zhang, G.2
  • 34
    • 0001363544 scopus 로고
    • Classes of domains and imbedding theorems for function spaces
    • V.G. Maz’ya, Classes of domains and imbedding theorems for function spaces, Dokl. Akad. Nauk. SSSR 133 (1960) 527-530.
    • (1960) Dokl. Akad. Nauk. SSSR , vol.133 , pp. 527-530
    • Maz’ya, V.G.1
  • 35
    • 0000190919 scopus 로고
    • The isoperimetric inequality
    • R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978) 1182-1238.
    • (1978) Bull. Amer. Math. Soc , vol.84 , pp. 1182-1238
    • Osserman, R.1
  • 37
    • 0003333144 scopus 로고
    • Convex Bodies: The Brunn-Minkowski Theory
    • Cambridge University Press, Cambridge
    • R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, 44, Cambridge University Press, Cambridge, 1993.
    • (1993) Encyclopedia of Mathematics and Its Applications , vol.44
    • Schneider, R.1
  • 39
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • G. Talenti, Best constant in Sobolev inequality Ann. Mat. Pura. Appl. 110 (1976) 353-372.
    • (1976) Ann. Mat. Pura. Appl , vol.110 , pp. 353-372
    • Talenti, G.1
  • 41
    • 0038008864 scopus 로고    scopus 로고
    • Sobolev inequality for measure space
    • Hsinchu, 1990-1991, Internat. Press, Cambridge, MA
    • S.-T. Yau, Sobolev inequality for measure space, Tsing Hua lectures on geometry and analysis (Hsinchu, 1990-1991), 299-313, Internat. Press, Cambridge, MA, 1997.
    • (1997) Tsing Hua Lectures on Geometry and Analysis , pp. 299-313
    • Yau, S.-T.1
  • 42
    • 0001846041 scopus 로고    scopus 로고
    • The affine Sobolev inequality
    • G. Zhang, The affine Sobolev inequality, J. Differential Geom. 53 (1999) 183-202.
    • (1999) J. Differential Geom , vol.53 , pp. 183-202
    • Zhang, G.1


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