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Volumn 83, Issue 1, 2009, Pages 1-26

General Lp affine isoperimetric inequalities

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EID: 70349798879     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1253804349     Document Type: Article
Times cited : (355)

References (52)
  • 1
    • 0033416837 scopus 로고    scopus 로고
    • Continuous rotation invariant valuations on convex sets
    • S. Alesker, Continuous rotation invariant valuations on convex sets, Ann. of Math. (2) 149 (1999) 977-1005.
    • (1999) Ann. of Math. , vol.2 , Issue.149 , pp. 977-1005
    • Alesker, S.1
  • 2
    • 0035611289 scopus 로고    scopus 로고
    • Description of translation invariant valuations on convex sets with solution of P. McMullen’s conjecture
    • S. Alesker, Description of translation invariant valuations on convex sets with solution of P. McMullen’s conjecture, Geom. Funct. Anal. 11 (2001) 244-272.
    • (2001) Geom. Funct. Anal , vol.11 , pp. 244-272
    • Alesker, S.1
  • 3
    • 0142138740 scopus 로고    scopus 로고
    • Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations
    • S. Alesker, Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations, J. Differential Geom. 63 (2003) 63-95.
    • (2003) J. Differential Geom , vol.63 , pp. 63-95
    • Alesker, S.1
  • 4
    • 34047171939 scopus 로고    scopus 로고
    • Valuations on manifolds and Rumin cohomology
    • A. Bernig & L. Brocker, Valuations on manifolds and Rumin cohomology, J. Differential Geom. 75 (2007) 433-457.
    • (2007) J. Differential Geom , vol.75 , pp. 433-457
    • Bernig, A.1    Brocker, L.2
  • 5
    • 0012570201 scopus 로고
    • Projection bodies, Geometric aspects of functional analysis (1986/87)
    • (J. Lindenstrauss and V. D. Milman, eds.), Springer, Berlin
    • J. Bourgain & J. Lindenstrauss, Projection bodies, Geometric aspects of functional analysis (1986/87) (J. Lindenstrauss and V. D. Milman, eds.), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 250-270.
    • (1988) Lecture Notes in Math , vol.1317 , pp. 250-270
    • Bourgain, J.1    Lindenstrauss, J.2
  • 6
    • 0037091874 scopus 로고    scopus 로고
    • The Lp-Busemann-Petty centroid inequality
    • p-Busemann-Petty centroid inequality, Adv. Math. 167 (2002) 128-141.
    • (2002) Adv. Math , vol.167 , pp. 128-141
    • Campi, S.1    Gronchi, P.2
  • 7
    • 33746888293 scopus 로고    scopus 로고
    • The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry
    • p-Minkowski problem and the Minkowski problem in centroaffine geometry, Adv. Math. 205 (2006) 33-83.
    • (2006) Adv. Math , vol.205 , pp. 33-83
    • Chou, K.S.1    Wang, X.J.2
  • 9
    • 0004182159 scopus 로고    scopus 로고
    • Second ed., Cambridge University Press, Cambridge
    • R. J. Gardner, Geometric tomography, Second ed., Cambridge University Press, Cambridge, 2006.
    • (2006) Geometric Tomography
    • Gardner, R.J.1
  • 10
    • 0039529094 scopus 로고    scopus 로고
    • P-cross-section bodies Indiana Univ
    • R. J. Gardner & A. Giannopoulos, p-cross-section bodies Indiana Univ. Math. J. 48 (1999) 593-613.
    • (1999) Math. J , vol.48 , pp. 593-613
    • Gardner, R.J.1    Giannopoulos, A.2
  • 11
    • 0005899134 scopus 로고    scopus 로고
    • Affine inequalities and radial mean bodies Amer
    • R. J. Gardner & G. Zhang, Affine inequalities and radial mean bodies Amer. J. Math. 120 (1998) 505-528.
    • (1998) J. Math , vol.120 , pp. 505-528
    • Gardner, R.J.1    Zhang, G.2
  • 12
    • 0007236082 scopus 로고    scopus 로고
    • Convolutions, transforms, and convex bodies
    • E. Grinberg & G. Zhang, Convolutions, transforms, and convex bodies, Proc. London Math. Soc. (3) 78 (1999) 77-115.
    • (1999) Proc. London Math. Soc. , vol.3 , Issue.78 , pp. 77-115
    • Grinberg, E.1    Zhang, G.2
  • 13
    • 2942731105 scopus 로고
    • Uber kennzeichnende Eigenschaften von euklidischen Raumen und Ellipsoiden I
    • P. M. Gruber, Uber kennzeichnende Eigenschaften von euklidischen Raumen und Ellipsoiden I, J. Reine Angew. Math. 265 (1974) 61-83.
    • (1974) J. Reine Angew. Math , vol.265 , pp. 61-83
    • Gruber, P.M.1
  • 15
    • 39749104135 scopus 로고    scopus 로고
    • Lp intersection bodies
    • p intersection bodies, Adv. Math. 217 (2008) 2599-2624.
    • (2008) Adv. Math , vol.217 , pp. 2599-2624
    • Haberl, C.1
  • 17
    • 33748605985 scopus 로고    scopus 로고
    • Blaschke and Minkowksi endomorphisms of convex bodies
    • M. Kiderlen, Blaschke and Minkowksi endomorphisms of convex bodies, Trans. Amer. Math. Soc. 358 (2006) 5539-5564.
    • (2006) Trans. Amer. Math. Soc , vol.358 , pp. 5539-5564
    • Kiderlen, M.1
  • 19
    • 0037176336 scopus 로고    scopus 로고
    • Projection bodies and valuations
    • M. Ludwig, Projection bodies and valuations, Adv. Math. 172 (2002) 158-168.
    • (2002) Adv. Math , vol.172 , pp. 158-168
    • Ludwig, M.1
  • 20
    • 0042575606 scopus 로고    scopus 로고
    • Ellipsoids and matrix valued valuations, Duke
    • M. Ludwig, Ellipsoids and matrix valued valuations, Duke Math. J. 119 (2003) 159-188.
    • (2003) Math. J , vol.119 , pp. 159-188
    • Ludwig, M.1
  • 21
    • 26444584569 scopus 로고    scopus 로고
    • Minkowski valuations
    • M. Ludwig, Minkowski valuations, Trans. Amer. Math. Soc. 357 (2005) 4191-4213.
    • (2005) Trans. Amer. Math. Soc , vol.357 , pp. 4191-4213
    • Ludwig, M.1
  • 22
    • 33845887583 scopus 로고    scopus 로고
    • Intersection bodies and valuations
    • M. Ludwig, Intersection bodies and valuations, Amer. J. Math. 128 (2006) 1409-1428.
    • (2006) Amer. J. Math , vol.128 , pp. 1409-1428
    • Ludwig, M.1
  • 23
    • 0000537779 scopus 로고    scopus 로고
    • A characterization of affine surface area
    • M. Ludwig & M. Reitzner, A characterization of affine surface area, Adv. Math. 147 (1999) 138-172.
    • (1999) Adv. Math , vol.147 , pp. 138-172
    • Ludwig, M.1    Reitzner, M.2
  • 24
    • 70350259922 scopus 로고    scopus 로고
    • A classification of SL(N) invariant valuations
    • press
    • M. Ludwig & M. Reitzner, A classification of SL(n) invariant valuations, Ann. Math. (2), in press.
    • Ann. Math , vol.2
    • Ludwig, M.1    Reitzner, M.2
  • 25
    • 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
  • 26
    • 84960569190 scopus 로고
    • Centroid bodies and dual mixed volumes
    • E. Lutwak, Centroid bodies and dual mixed volumes, Proc. Lond. Math. Soc. 60 (1990) 365-391.
    • (1990) Proc. Lond. Math. Soc. , vol.60 , pp. 365-391
    • Lutwak, E.1
  • 27
    • 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
  • 28
    • 0030600832 scopus 로고    scopus 로고
    • The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
    • E. Lutwak, The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas, Adv. Math. 118 (1996) 244-294.
    • (1996) Adv. Math , vol.118 , pp. 244-294
    • Lutwak, E.1
  • 29
    • 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
    • 0034664274 scopus 로고    scopus 로고
    • A new ellipsoid associated with convex bodies, Duke
    • E. Lutwak, D. Yang, & G. Zhang, A new ellipsoid associated with convex bodies, Duke Math. J. 104 (2000) 375-390.
    • (2000) Math. J , vol.104 , pp. 375-390
    • Lutwak, E.1    Yang, D.2    Zhang, G.3
  • 34
    • 0031227458 scopus 로고    scopus 로고
    • Blaschke-Santalo inequalities
    • E. Lutwak & G. Zhang, Blaschke-Santalo inequalities, J. Differential Geom. 47 (1997) 1-16.
    • (1997) J. Differential Geom , vol.47 , pp. 1-16
    • Lutwak, E.1    Zhang, G.2
  • 36
    • 33846813628 scopus 로고    scopus 로고
    • Concentration of mass on isotropic convex bodies, Geom
    • G. Paouris, Concentration of mass on isotropic convex bodies, Geom. Funct. Anal. 16 (2006) 1021-1049.
    • (2006) Funct. Anal , vol.16 , pp. 1021-1049
    • Paouris, G.1
  • 37
    • 0000324842 scopus 로고
    • Centroid surfaces
    • C. M. Petty, Centroid surfaces, Pacific J. Math. 11 (1961) 1535-1547.
    • (1961) Pacific J. Math , vol.11 , pp. 1535-1547
    • Petty, C.M.1
  • 38
    • 0002344844 scopus 로고
    • Isoperimetric problems
    • (Univ. Oklahoma, 1971), University of Oklahoma
    • C. M. Petty, Isoperimetric problems, Proc. Conf. Convexity and Combinatorial Geometry (Univ. Oklahoma, 1971), University of Oklahoma, 1972, 26-41.
    • (1972) Proc. Conf. Convexity and Combinatorial Geometry , pp. 26-41
    • Petty, C.M.1
  • 39
    • 39749094149 scopus 로고    scopus 로고
    • Generalized Minkowski-Funk transforms and small denominators on the sphere
    • B. Rubin, Generalized Minkowski-Funk transforms and small denominators on the sphere, Fract. Calc. Appl. Anal. 3 (2000) 177-203.
    • (2000) Fract. Calc. Appl. Anal , vol.3 , pp. 177-203
    • Rubin, B.1
  • 40
    • 4944246828 scopus 로고    scopus 로고
    • The Fourier transform and Firey projections of convex bodies
    • Indiana Univ
    • D. Ryabogin & A. Zvavitch, The Fourier transform and Firey projections of convex bodies, Indiana Univ. Math. J. 53 (2004) 667-682.
    • (2004) Math. J , vol.53 , pp. 667-682
    • Ryabogin, D.1    Zvavitch, A.2
  • 41
    • 84968495638 scopus 로고
    • Equivariant endomorphisms of the space of convex bodies
    • R. Schneider, Equivariant endomorphisms of the space of convex bodies, Trans. Amer. Math. Soc. 194 (1974) 53-78.
    • (1974) Trans. Amer. Math. Soc , vol.194 , pp. 53-78
    • Schneider, R.1
  • 43
    • 33845898811 scopus 로고    scopus 로고
    • Rotation equivariant Minkowski valuations
    • R. Schneider & F. E. Schuster, Rotation equivariant Minkowski valuations, Int. Math. Res. Not. (2006), Article ID 72894, 20 pages.
    • (2006) Int. Math. Res. Not , pp. 20
    • Schneider, R.1    Schuster, F.E.2
  • 45
    • 39049093357 scopus 로고    scopus 로고
    • Convolutions and multiplier transformations
    • F. E. Schuster, Convolutions and multiplier transformations, Trans. Amer. Math. Soc. 359 (2007) 5567-5591.
    • (2007) Trans. Amer. Math. Soc , vol.359 , pp. 5567-5591
    • Schuster, F.E.1
  • 46
    • 3242875430 scopus 로고    scopus 로고
    • Surface bodies and p-affine surface area
    • C. Schütt & E. Werner, Surface bodies and p-affine surface area, Adv. Math. 187 (2004) 98-145.
    • (2004) Adv. Math , vol.187 , pp. 98-145
    • Schütt, C.1    Werner, E.2
  • 47
    • 0037091516 scopus 로고    scopus 로고
    • The discrete planar L0-Minkowski problem
    • 0-Minkowski problem, Adv. Math. 167 (2002) 160-174.
    • (2002) Adv. Math , vol.167 , pp. 160-174
    • Stancu, A.1
  • 48
    • 0346269039 scopus 로고    scopus 로고
    • On the number of solutions to the discrete two-dimensional Lo-Minkowski problem
    • A. Stancu, On the number of solutions to the discrete two-dimensional Lo-Minkowski problem, Adv. Math. 180 (2003) 290-323.
    • (2003) Adv. Math , vol.180 , pp. 290-323
    • Stancu, A.1
  • 49
    • 39049104254 scopus 로고    scopus 로고
    • Subword complexity and projection bodies
    • C. Steineder, Subword complexity and projection bodies, Adv. Math. 217 (2008) 2377-2400.
    • (2008) Adv. Math , vol.217 , pp. 2377-2400
    • Steineder, C.1
  • 50
    • 0004236285 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge
    • A. C. Thompson, Minkowski geometry, Cambridge University Press, Cambridge, 1996.
    • (1996) Minkowski Geometry
    • Thompson, A.C.1
  • 51
    • 33747074835 scopus 로고    scopus 로고
    • Centroid bodies and comparison of volumes, Indiana Univ
    • V. Yaskin & M. Yaskina, Centroid bodies and comparison of volumes, Indiana Univ. Math. J. 55 (2006) 1175-1194.
    • (2006) Math. J , vol.55 , pp. 1175-1194
    • Yaskin, V.1    Yaskina, M.2
  • 52
    • 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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