TY - JOUR
T1 - Smooth solutions to the Lp dual Minkowski problem
AU - Chen, Chuanqiang
AU - Huang, Yong
AU - Zhao, Yiming
N1 - Funding Information:
Research of C. Chen was supported by ZJNSF No. LY17A010022 and NSFC No. 11771396. Research of Y. Huang was supported by the National Science Fund for Distinguished Young Scholars (No. 11625103) and Tian Yuan Special Foundation (11826014), the Fundamental Research Funds for the Central Universities..
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - In this paper, we consider the Lp dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the Lp dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.
AB - In this paper, we consider the Lp dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the Lp dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.
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U2 - 10.1007/s00208-018-1727-3
DO - 10.1007/s00208-018-1727-3
M3 - Article
AN - SCOPUS:85049864371
SN - 0025-5831
VL - 373
SP - 953
EP - 976
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -