The Existence of Convex Body with Prescribed Curvature Measures

By Pengfei Guan, Changshou Lin, Xinan Ma. 2009

83 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0ad8b62198dd3be4a676fb8ac5796f7563a38ea8

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In Applied Mathematics

1. Zhizhang Wang
2. Changyu Ren
3. Yiming Zhao
4. H. Jiao
5. Yong Huang
6. Junfang Li
7. Pengfei Guan
8. Jianchun Chu

In Geometry and Topology

1. Zhizhang Wang
2. Changyu Ren
3. Yiming Zhao
4. Junfang Li
5. J. Spruck
6. Pengfei Guan
7. H. Jiao
8. Ling Xiao

Citations in the corpus

• Global C2‐Estimates for Convex Solutions of Curvature Equations (2013, background): “C2 estimate was also proved for equation of prescribing curvature measures problem in [15, 14], where f(X, ν) = 〈X, ν〉f̃(X).”
• The global curvature estimate for the n-2 Hessian equation (2020, methodology): “The curvature estimate was also established for the equation of the prescribing curvature measure problem by Guan-Li-Li [24] and Guan-Lin-Ma [23].”
• Hypersurfaces of prescribed curvature measure (2011, background): “Recently, with certain assumptions on f , Guan-Lin-Ma obtained the existence and regularity of convex solutions in [11].”
• On the L dual Minkowski problem (2018, background): “1, we first show the uniqueness part as [25,57].”
• A note on starshaped compact hypersurfaces with a prescribed scalar curvature in space forms (2015, methodology): “In this section, we follow the idea of [3] and [6] to derive C(1) estimates for the height function ρ.”
• The $L_p$-Aleksandrov problem for $L_p$-integral curvature (2018, unknown): “, Guan–Lin–Ma [18] and Guan–Li–Li [19].”
• Existence of solutions to the even dual Minkowski problem (2018, unknown): “Progress on this problem was made by Guan, Li & Li [24] and Guan, Lin & Ma [26].”
• Curvature estimates for a class of Hessian type equations (2020, background): “onstant C depending only on n, k, infM ρ, supM ρ, inf f and kfkC1 such that (4.1) |∇ρ| 6 C, where ∇ denotes the gradient on Sn. Proof. By (3.1), it suffices to obtain a positive lower bound of u. As in [13], we consider the following quantity w = −logu+γ(|X|2), where γ is a single-variable function to”
• On the curvature estimates for Hessian equations (2016, background): “C2 estimate was also proved for equation of prescribing curvature measures problem in [20, 19], where f(X, ν) = 〈X, ν〉f̃(X).”
• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “See Guan-Lin-Ma [36] and the recent work of Guan-Li-Li [38] on this problem.”