May  2013, 33(5): 1975-1986. doi: 10.3934/dcds.2013.33.1975

Two problems related to prescribed curvature measures

1. 

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China, China

Received  March 2012 Revised  September 2012 Published  December 2012

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. Moreover, we promote Ivochkina's $C^2$ estimates for prescribed curvature equation in [12,13].
Citation: Yong Huang, Lu Xu. Two problems related to prescribed curvature measures. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 1975-1986. doi: 10.3934/dcds.2013.33.1975
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show all references

References:
[1]

in "Current Topics in Partial Differential Equations" (Kinokuniya, Tokyo.), (1986), 1-26.  Google Scholar

[2]

Comm. Pure Appl. Math., 41 (1988), 47-70. doi: 10.1002/cpa.3160410105.  Google Scholar

[3]

Series in Geometry and Topology, 39. International Press, Somerville, MA, 2006.  Google Scholar

[4]

Lecture Notes, 147-page Manuscript (2004). Available from: http://www.math.mcgill.ca/guan/zheda0508.pdf. Google Scholar

[5]

P. Guan, Private, notes., ().   Google Scholar

[6]

Ann. of Math., 156 (2002), 655-673. doi: 10.2307/3597202.  Google Scholar

[7]

Comm. Pure Appl. Math., 50 (1997), 789-811. doi: 10.1002/(SICI)1097-0312(199708)50:8<789::AID-CPA4>3.3.CO;2-B.  Google Scholar

[8]

notes, 1995. Google Scholar

[9]

Duke Math. J., 161 (2012), 1927-1942. Google Scholar

[10]

Int. Math. Res. Not. IMRN, 11 (2009), 1947-1975. doi: 10.1093/imrn/rnp007.  Google Scholar

[11]

Second Edition, Revised Third Printing, Springer-Verlag, 1998.  Google Scholar

[12]

Mathematics of the USSR-Sbornik, 67 (1990), 317-339.  Google Scholar

[13]

Leningrad Math. J., 2 (1991), 192-217.  Google Scholar

[14]

Trans. Amer. Math. Soc., 347 (1995), 857-895. doi: 10.2307/2154876.  Google Scholar

[15]

Bull. Austral. Math. Soc., 50 (1994), 317-326. Google Scholar

[16]

" Sem. Inst. Mate. Appl. Giovanni Sansone," Univ. Studi Firenze, (1983). Google Scholar

[17]

translated from the Russian by Israel Program for Scientific Translations, Amer. Math. Soc., Providence, RI, 1973.  Google Scholar

[18]

Encyclopedia of Mathematics and its Applications, 44, Cambridge Univ. Press, Cambridge, 1993. doi: 10.1017/CBO9780511526282.  Google Scholar

[19]

Duke Math. J., 123 (2004), 235-264. doi: 10.1215/S0012-7094-04-12321-8.  Google Scholar

[20]

Calc. Var. Partial Differential Equations, 26 (2006), 357-377. doi: 10.1007/s00526-006-0011-7.  Google Scholar

[21]

Arch. Rational Mech. Anal., 111 (1990), 153-179. doi: 10.1007/BF00375406.  Google Scholar

[22]

J. Reine Angew. Math., 519 (2000), 41-57. doi: 10.1515/crll.2000.016.  Google Scholar

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