| 1 | Aubin T . Problemes isopérimétriques et espaces de Sobolev. J Differential Geom, 1976, 11 (4): 573- 598 |
| 2 | Banchoff T F , Pohl W F . A generalization of the isoperimetric inequality. J Differential Geom, 1971, 6 (2): 175- 192 |
| 3 | Blaschke W . Vorlesungen über Differentialgeometrie, II: Affine Differentialgeometrie. Berlin: Springer, 1923 |
| 4 | Bonnesen T . über eine Versch?rfung der isoperimetrischen Ungleichheit des Kreises in der Ebene und auf der Kugeloberfl?che nebst einer Anwendung auf eine Minkowskische Ungleichheit für konvexe K?rper. Math Ann, 1921, 84 (3): 216- 227 |
| 5 | B?r?czky K J , Lutwak E , Yang D , Zhang G . The log-Brunn-Minkowski inequality. Adv Math, 2012, 231 (3): 1974- 1997 |
| 6 | Bottema O . Eine obere Grenze für das isoperimetrische Defizit ebener Kurven. Nederl Akad Wetensch Proc, 1933, 36, 442- 446 |
| 7 | Burago Y D , Zalgaller V A . Geometric Inequalities. Berlin: Springer Science & Business Media, 2013 |
| 8 | Chlebík M , Cianchi A , Fusco N . The perimeter inequality under Steiner symmetrization: cases of equality. Ann Math, 2005, 162 (1): 525- 555 |
| 9 | Fusco N , Maggi F , Pratelli A . The sharp quantitative isoperimetric inequality. Ann Math, 2008, 168, 941- 980 |
| 10 | Gardner R J . Geometric Tomography. Cambridge: Cambridge University Press, 1995 |
| 11 | Green M , Osher S . Steiner polynomials, Wulff flows, and some new isoperimetric inequalities for convex plane curves. Asian J Math, 1999, 3, 659- 676 |
| 12 | Haberl C , Schuster F E . General Lp affine isoperimetric inequalities. J Differential Geom, 2009, 83, 1- 26 |
| 13 | Hadwiger H . Die isoperimetrische Ungleichung im Raum. Elem Math, 1948, 3, 25- 38 |
| 14 | Hadwiger H . Vorlesungen über Inhalt, Oberfl?che und Isoperimetrie. Berlin: Springer-Verlag, 2013 |
| 15 | Hardy G H , Littlewood J E , Pólya G . Inequalities. Cambridge: Cambridge University Press, 1952 |
| 16 | Howard R . The sharp Sobolev inequality and the Banchoff-Pohl inequality on surfaces. Proc Amer Math Soc, 1998, 126 (9): 2779- 2787 |
| 17 | Hsiung C C . Isoperimetic inequalities for two-dimensional Riemannian manifolds with boundary. Ann Math, 1961, 73 (2): 213- 220 |
| 18 | Hug D . Curvature relations and affine surface area for a general convex body and its polar. Results Math, 1996, 29, 233- 248 |
| 19 | Klain D A . Bonnesen-type inequalities for surfaces of constant curvature. Adv Appl Math, 2007, 39 (2): 143- 154 |
| 20 | Klain D A , Rota G C . Introduction to geometric probability. Cambridge: Cambridge University Press, 1997 |
| 21 | Leichtwei? K . Affine Geometry of Convex Bodies. Heidelberg: Johann Ambrosius Barth, 1998 |
| 22 | Lutwak E . Dual mixed volumes. Pacific J Math, 1975, 58 (2): 531- 538 |
| 23 | Lutwak E . On the Blaschke-Santaló inequality. Ann New York Acad Sci, 1985, 440 (1): 106- 112 |
| 24 | Lutwak E . On some affine isoperimetric inequalities. J Differential Geom, 1986, 23, 1- 13 |
| 25 | Lutwak E . Mixed affine surface area. J Math Anal Appl, 1987, 125, 351- 360 |
| 26 | Lutwak E . Extended affine surface area. Adv Math, 1991, 85 (1): 39- 68 |
| 27 | Lutwak E . The Brunn-Minkowski-Firey theory I. Mixed volumes and the Minkowski problem. J Differential Geom, 1993, 38 (1): 131- 150 |
| 28 | Lutwak E . The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas. Adv Math, 1996, 118, 244- 294 |
| 29 | Lutwak E , Yang D , Zhang G . Lp affine isoperimetric inequalities. J Differential Geom, 2000, 56, 111- 132 |
| 30 | Lutwak E , Yang D , Zhang G . Sharp affine Lp Sobolev inequalities. J Differential Geom, 2002, 62 (1): 17- 38 |
| 31 | Montiel S , Ros A . Compact hypersurfaces: the Alexandrov theorem for higher order mean curvature. J Differential Geom, 1991, 52, 279- 296 |
| 32 | Osserman R . The isoperimetric inequality. Bull Amer Math Soc, 1978, 84 (6): 1182- 1238 |
| 33 | Osserman R . Bonnesen-style isoperimetric inequalities. Amer Math Monthly, 1979, 86, 1- 29 |
| 34 | Pan S , Xu H . Stability of a reverse isoperimetric inequality. J Math Anal Appl, 2009, 350 (1): 348- 353 |
| 35 | Petty C M. Isoperimetric problems[C]//Proc Conf Convexity Combinat Geom. University of Oklahoma, Norman, Okla, 1971: 26-41 |
| 36 | Petty C M . Geominimal surface area. Geom Dedicata, 1974, 3, 77- 97 |
| 37 | Petty C M . Affine isoperimetric problems. Ann New York Acad Sci, 1985, 440, 113- 127 |
| 38 | Pleijel A . On konvexa kurvor. Nordisk Math Tidskr, 1955, 3, 57- 64 |
| 39 | Ren D . Topics in Integral Geometry. Singapore: World Scientific, 1994 |
| 40 | Santaló L A . Un invariante afin para los cuerpos convexos del espacio de n dimensiones. Portugaliae Math, 1949, 8, 155- 161 |
| 41 | Santaló L . Integral formulas in Crofton's style on the sphere and some inequalities referring to spherical curves. Duke Math J, 1942, 9, 707- 722 |
| 42 | Santaló L . Integral Geometry and Geometric Probability. Cambredge: Cambridge University Press, 2004 |
| 43 | Santaló L . Integral geometry on surfaces of constant negative curvature. Duke Math J, 1943, 10 (4): 687- 704 |
| 44 | Schmidt E . über die isoperimetrische Aufgabe imn-dimensionalen Raum konstanter negativer Krümmung. Math Zeit, 1939, 46 (1): 204- 230 |
| 45 | Schneider R . Convex bodies: the Brunn-Minkowski theory. Cambridge: Cambridge University Press, 2014 |
| 46 | Schirokow P A , Schirokow A P . Affine Differential Geometrie. Leipzig: Teubner, 1962 |
| 47 | Werner E , Ye D . New Lp affine isperimetric inequalities. Adv Math, 2008, 218, 762- 780 |
| 48 | Xu W , Zhou J , Zhu B . On Bonnesen-type inequalities for a surface of constant curvature. Proc Amer Math Soc, 2015, 143 (11): 4925- 4935 |
| 49 | Ye D . Inequalities for general mixed affine surface areas. J London Math Soc, 2012, 85 (2): 101- 120 |
| 50 | Zhang G. Geometric inequalities and inclusion measures of convex bodies Mathematika, 1994, 41(1): 95-116 |
| 51 | Zhang G . The affine Sobolev inequality. J Differential Geom, 1999, 53 (1): 183- 202 |
| 52 | Zhang G . A lecture on Integral Geometry. Proceedings of the Fourteenth Internatioanl Workshop on Diff Geom, 2010, 14, 13- 30 |
| 53 | Zhang G, Zhou J. Containment measures in integral geometry//Grinberg E, Li S, Zhang G, Zhou J. Integral Geometry and Convexity. Singapore: World Scientific, 2006: 153-168 |
| 54 | 赵长健. 凸体与星体混合的等周不等式. 数学物理学报, 2019, 39 (5): 993- 1000 |
| 54 | Zhao C J . On isoperimetric inequality for mixture of convex and star bodies. Acta Math Sci, 2019, 39 (5): 993- 1000 |
| 55 | 周家足. 平面Bonnesen -型不等式. 数学学报, 2007, 50 (6): 1397- 1402 |
| 55 | Zhou J Z . On Bonnesen-type inequalities. Acta Math Sin, 2007, 50 (6): 1397- 1402 |
| 56 | 周家足, 任德麟. 从积分几何的观点看几何不等式. 数学物理学报, 2010, 30 (5): 1322- 1339 |
| 56 | Zhou J Z , Ren D L . Geometric inequalities: From integral geometry point of view. Acta Math Sci, 2010, 30 (5): 1322- 1339 |
| 57 | Zhu B , Li N , Zhou J . Isoperimetric inequalities for Lp geominimal surface area. Glasgow Math J, 2011, 53 (3): 717- 726 |
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