[1]  Banchoff  T F, Pohl W F. A generalization of the isoperimetric inequality. J Diff Geo, 1971, 6: 175--213

[2]  Blaschke W.  Vorlesungen \"uber Intergralgeometrie. Berlin: Deutsch Verlag Wiss, 1955

[3]  Bokowski J, Heil E. Integral representation of  quermassintegrals and Bonnesen-style inequalities. Arch Math, 1986, 47: 79--89

[4]  Bonnesen T. Les Problèms des Isopèrimètres et des Isèpiphanes. Paris: Gauthier-Villars, 1929

[5]  Bonnesen T, Fenchel W. Theorie der Konvexen K\"oeper. Berlin, New York: Springer-Verlag, 1974

[6]  Bottema O. Eine obere Grenze f\"ur das isoperimetrische Defizit ebener Kurven. Nederl Akad Wetensch Proc, 1933, A66: 442--446

[7]  Burago Yu D, Zalgaller V A. Geometric Inequalities. Berlin Heidelberg: Springer-Verlag, 1988

[8]  Chen W, Howard R, Lutwark E, Yang D, Zhang G. A generalized affine isoperimetric inequality. J Geom Anal, 2004, 14(4):  597--612

[9]  Croke C. A sharp four-dimensional isoperimetric inequality. Comment Math Helv, 1984, 59(2): 187--192

[10]  Dai Y, Zhou J. Two new Bonnesen type inequalities. preprint

[11]  Diskant V.  A generalization of Bonnesen's inequalities. Soviet Math Dokl, 1973, 14: 1728--1731

[12]  Enomoto K. A generalization of the isoperimetric inequality on S² and flat tori in S³. Proc Amer Math Soc, 1994, 120(2):  553--558

[13]  Flanders  H. A proof of Minkowski's inequality for convex curves. Amer Math Monthly, 1968, 75: 581--593

[14]  Gage M. An isoperimetric inequality with applications to curve shortening. Duke Math J, 1983, 50(4): 1225--1229

[15]  Gardner R. Geometric Tomography. New York: Cambridge Univ Press, 1995

[16]  Green M, Osher S. Steiner polynomials, Wulff flows, and some new isoperimetric inequalities for convex plane curves. Asian J Math, 1999,  3(3): 659--676

[17]  Grinberg  E, Li S, Zhang G, Zhou J. Integral Geometry and Convexity, Proceedings of the International Conference. Singapore: World Scientific, 2006

[18]  Grinberg E, Ren D, Zhou J. The symetric isoperimetric deficit and the containment problem in a plan of constant curvature. preprint

[19]  Grinberg E. Isoperimetric inequalities and identities for k-dimensional cross-sections of convex bodies. Math Ann, 1991, 291:  75--86

[20]  Grinberg E,  Zhang G. Convolutions, transforms, and convex bodies. Proc London Math Soc, 1999, 78:  7--115

[21]  Gysin L. The isoperimetric inequality for nonsimple closed curves. Proc Amer Math Soc, 1993, 118(1): 197--203

[22]  Hadwiger H. Die isoperimetrische Ungleichung in Raum. Elemente Math, 1948, 3:  25--38

[23]  Hadwiger H. Vorlesungen \"uber Inhalt, Oberfl"ache und Isoperimetrie. Berlin: Springer, 1957

[24]  Hardy G, Littlewood J E, Polya G. Inequalities. Cambradge, New York: Cambradge Univ Press, 1951

[25]  Howard R. The sharp Sobolev inequality and the Banchoff-Pohl inequality on surfaces. Proc Amer Math Soc, 1998, 126: 2779--2787

[26]  Hsiung C C. Isoperimetric inequalities for two-dimensional Riemannian manifolds with boundary. Ann of Math, 1961, 73(2):  213--220

[27]  Hsiang  W Y. An elementary proof of the isoperimetric problem. Chin Ann Math, 2002, 23A(1):  7--12

[28]  Klain D. Bonnesen-type inequalities for surfaces of constant curvature. Advances in Applied Mathematics, 2007, 39(2): 143--154

[29]  Kotlyar B D. On a geometric inequality. (UDC513:519.21) Ukrainskii Geometricheskii Sbornik, 1987, 30: 49--52

[30]  Ku H, Ku  M, Zhang X. Isoperimetric inequalities on surfaces of constant curvature. Canadian J of Math, 1997, 49: 1162--1187

[31]  Li M, Zhou J. An upper limit for the isoperimetric deficit of convex set in a plane of constant curvature. Science China Mathematics, 2010, 53(8): 1941--1946

[32]  Li  P, Yau  S T. A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces.  Invent Math, 1982, 69:  269--291

[33]  Lutwak E, Yang D, Zhang G. Sharp affine L_p Sobolev inequality. J Diff Geom, 2002, 62:  17--38

[34]  Ma L, Zhou J. On Ros' type isoperimetric inequalities. preprint

[35]  Ma  L, Zhou J. On the curvature integrals of the plane oval. preprint

[36]  Osserman R. The isoperimetric inequality. Bull Amer Math Soc, 1978, 84: 1182--1238

[37]  Osserman R. Bonnesen-style isoperimetric inequality. Amer Math Monthly, 1979, 86:  1--29

[38]  Pleijel A. On konvexa kurvor. Nordisk Math Tidskr, 1955, 3: 57--64

[39]  Polya G, Szego G. Isoperimetric inequalities in mathematical physics. Ann of Math Studies. Princeton: Princeton Univ, 1951: 27 

[40]  Ren D. Topics in Integral Geometry. Singapore: World Scientific, 1994

[41]  Sangwine, Yager J R. Mixe Volumes, Handbook of Covex Geometry. North-Holland:  Wills, 1993: 43--71

[42]  Santalò L A. Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976

[43]  Schneider R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge: Cambridge Univ Press, 1993

[44]  Stone A. On the isoperimetric inequality on a minimal surface. Calc Var Partial Diff Equations, 2003, 17(4): 369--391

[45]  Tang D. Discrete Wirtinger and isoperimetric type inequalities. Bull Austral Math Soc, 1991, 43: 467--474

[46]  Teufel E. A generalization of the isoperimetric inequality in the hyperbolic plane. Arch Math, 1991, 57(5):   508--513

[47]  Teufel E. Isoperimetric inequalities for closed curves in spaces of constant curvature. Results Math, 1992, 22:  622--630

[48]  Wei  S, Zhu  M. Sharp isoperimetric inequalities and sphere theorems. Pacific J Math, 2005, 220(1):  183--195

[49]  Weiner J L. A generalization of the isoperimetric inequality on the 2-sphere. Indiana Univ Math Jour, 1974, 24:  243--248

[50]  Weiner J L. Isoperimetric inequalities for immersed closed spherical curves. Proc Amer Math Soc, 1994, 120(2):  501--506

[51]  Yau S T. Isoperimetric constants and the first eigenvalue of a compact manifold. Ann Sci Ec Norm Super, 1975, 8(4): 487--507

[52]  Zhang G. The affine Sobolev inequality. J Diff Geom, 1999, 53: 183--202

[53]  Zhang G. Geometric inequalities and inclusion measures of convex bodies. Mathematika, 1994, 41:  95--116

[54]  Zhang G, Zhou J. Containment Measures in Integral Geometry. Integral Geometry and Convexity. Singapore: World Scientific, 2006: 153--168

[55]  Zhang G. Convex Geometric Analysis. preprint

[56]  Zhang X M. Bonnesen-style inequalities and Pseudo-perimeters for polygons. J Geom, 1997, 60:  188--201

[57]  Zhang X M. Schur-convex functions and isoperimetric inequalities. Proc Amer Math Soc, 1998, 126(2):  461--470

[58]  Zhou J,  Chen F.  The Bonneesen-type inequality in a plane of constant cuvature. J Korean Math Soc, 2007, 44(6): 1363--1372

[59]  Zhou J. A kinematic formula and analogous of Hadwiger's theorem in space. Contemporary Math, 1992, 140:  159--167

[60]  Zhou J. The sufficient condition for a convex domain to contain another in R⁴. Proc Amer Math Soc, 1994, 121:  907--913

[61]  Zhou J. Kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger's theorem in R²ⁿ. Trans Amer Math Soc, 1994, 345: 243--262

[62]  Zhou J.  When can one domain enclose another in R³? J Austral Math Soc (Series A), 1995, 59:  266--272

[63]  Zhou J. Sufficient conditions for one domain to contain another in a space of constant curvature. Proc Amer Math Soc, 1998, 126:  2797--2803

[64]  Zhou J. On Willmore Inequality for Submanifolds. Canadian Math Bul, 2007, 50(3):  474--480

[65]  Zhou J. On the Willmore deficit of convex surfaces. Lectures in Appl Math Amer Math Soc, 1994, 30: 279--287

[66]   Zhou J. The Willmore functional and the containment problem in R⁴. Science in China (Ser A), 2007, 50(3): 325--333

[67]  Zhou J. Plan Bonnesen-type inequalities. Acta Math Sinica (Chinese Series), 2007, 50(6):  397--1402

[68]  Zhou J,  Xia Y,  Zeng C. Some New Bonnesen-style inequalities. to appear in J Korean Math Soc

[69]  Zhou J, Ma L. The discrete isoperimetric deficit upper bound. preprint

[70]  Zhou J, Li M,  Ma L. The isoperimetric deficit upper bound for convex set in space. preprint

[71]  Zhou J,  Yue S, Ai W. On the isohomothetic inequalityies. preprint

[72]  Zhou J,  Zeng C,  Xia Y. On Minkowski style isohomothetic inequalities. preprint

[73]  Zhou J,  Du Y,  Cheng F. Some Bonnesen-style inequalities for higher dimensions. to appear in Acta Math Sinica

[74]  Zhou J. Curvature inequalities for curves. Inter J Comp Math Sci Appl, 2007, 1(2-4):  145--147

[75]  Zhou J, Zhou C, Ma F. Isoperimetric deficit upper limit of a planar convex set. Rendiconti del Circolo Matematico di Palermo (Serie II, Suppl), 2009, 81:  363--367