Isoperimetric inequalities for quermassintegrals

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1. [1] Yu D. Burago and V.A. Zalgaller, Geometric Inequalities, Springer-Verlag, Berlin, 1988. Zbl0633.53002MR936419
2. [2] H. Busemann, Convex Surfaces, Wiley Interscience, New York, 1958. Zbl0196.55101MR105155
3. [3] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Second edition, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
4. [4] N.M. Ivochkina, The Dirichlet problem for the equations of curvature of order, m. St Petersburg Math. J., 2, 1991, pp. 631-654. Zbl0732.35031MR1073214
5. [5] N.J. Korevaar, Sphere theorems via Aleksandrov for constant Weingarten curvature, J. Diff. Geom., 27, 1988, pp. 221-223. Zbl0638.53052
6. [6] P.L. Lions, N.S. Trudinger and J.J.E. Urbas, The Neumann problem for equations of Monge-Ampère type, Comm. Pure Appl. Math., 39, 1986, pp. 539-563. Zbl0604.35027MR840340
7. [7] R.C. Reilly, On the Hessian of a function and the curvatures of its graph, Michigan Math. J.20, 1973, pp. 373-383. Zbl0267.53003MR334045
8. [8] L. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, Cambridge, Mass., 1977. Zbl0342.53049MR433364
9. [9] N.S. Trudinger, On degenerate fully nonlinear equations in balls, Bull. Aust. Math. Soc., 35, 1987, pp. 299-307. Zbl0611.35028MR878440
10. [10] N.S. Trudinger, A priori bounds for graphs with prescribed curvature, In Analysis, etc., Academic Press, 1990, pp. 667-676. Zbl0714.53008MR1039367
11. [11] N.S. Trudinger, A priori bounds and necessary conditions for solvability of prescribed curvature equations, Manuscripta Math., 67, 1990, pp. 99-112. Zbl0703.35070MR1037998
12. [12] N.S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rat. Mech. Anal., 111, 1990, pp. 153-170. Zbl0721.35018MR1057653
13. [13] N.S. Trudinger, On the Dirichlet problem for Hessian equations, Aust. Nat. Univ. Centre for Math. and its Appl., Research Report M25, 1994. Zbl0887.35061MR1368245
14. [14] N.S. Trudinger, On new isoperimetric inequalities and symmetrization, in preparation. 
15. [15] N.S. Trudinger and J.J.E. Urbas, The Dirichlet problem for the equation of prescribed Gauss curvature, Bull. Aust. Math. Soc., 28, 1983, pp. 217-231. Zbl0524.35047MR729009

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