Curvature estimates for the level sets of solutions to the Monge-Ampère equation detD 2 u = 1

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-014-0864-6 ◽

2014 ◽

Vol 35 (6) ◽

pp. 895-906 ◽

Author(s):

Chuanqiang Chen ◽

Xinan Ma ◽

Shujun Shi

Keyword(s):

Curvature Estimates ◽

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Curvature estimates for the level sets of solutions to a class of Monge–Ampère equations

Nonlinear Analysis ◽

10.1016/j.na.2018.08.007 ◽

2019 ◽

Vol 178 ◽

pp. 337-347 ◽

Author(s):

Haiyu Feng ◽

Shujun Shi

Keyword(s):

Curvature Estimates ◽

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Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations

Journal of Partial Differential Equations ◽

10.4208/jpde.v25.n3.4 ◽

2012 ◽

Vol 25 (3) ◽

pp. 239-275 ◽

Author(s):

Wang Peihev and Zhang Wei

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Gaussian Curvature ◽

Elliptic Partial Differential Equations ◽

Partial Differential ◽

Nonlinear Elliptic ◽

Curvature Estimates

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Gaussian curvature estimates for the convex level sets of p-harmonic functions

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.20318 ◽

2010 ◽

Vol 63 (7) ◽

pp. 935-971 ◽

Author(s):

Xi-Nan Ma ◽

Qianzhong Ou ◽

Wei Zhang

Keyword(s):

Gaussian Curvature ◽

Harmonic Functions ◽

Curvature Estimates

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Principal curvature estimates for the convex level sets of semilinear elliptic equations

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2010.28.1151 ◽

2010 ◽

Vol 28 (3) ◽

pp. 1151-1164 ◽

Author(s):

Sun-Yung Alice Chang ◽

◽

Xi-Nan Ma ◽

Paul Yang ◽

Keyword(s):

Principal Curvature ◽

Elliptic Equations ◽

Semilinear Elliptic Equations ◽

Semilinear Elliptic ◽

Curvature Estimates

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The mean curvature estimate for the level sets of solutions of the Monge-Ampère equation on Riemannian manifold

Journal of Physics Conference Series ◽

10.1088/1742-6596/1941/1/012062 ◽

2021 ◽

Vol 1941 (1) ◽

pp. 012062

Author(s):

Xuemei Yu

Keyword(s):

Riemannian Manifold ◽

Mean Curvature ◽

Curvature Estimate ◽

The Mean ◽

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Gauss curvature estimates for the convex level sets of a minimal surface immersed in

Nonlinear Analysis ◽

10.1016/j.na.2011.05.051 ◽

2011 ◽

Vol 74 (16) ◽

pp. 5663-5677 ◽

Author(s):

Yunhua Ye

Keyword(s):

Minimal Surface ◽

Gauss Curvature ◽

Curvature Estimates

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Curvature estimates in dimensions 2 and 3 for the level sets of $p$-harmonic functions in convex rings

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-2012-05436-5 ◽

2012 ◽

Vol 364 (9) ◽

pp. 4605-4627 ◽

Author(s):

Jürgen Jost ◽

Xi-Nan Ma ◽

Qianzhong Ou

Keyword(s):

Harmonic Functions ◽

Curvature Estimates

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Principal curvature estimates for the level sets of harmonic functions and minimal graphs in $R^3$

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2011.10.225 ◽

2010 ◽

Vol 10 (1) ◽

pp. 225-243 ◽

Author(s):

Xi-Nan Ma ◽

Jiang Ye ◽

Yun-Hua Ye

Keyword(s):

Principal Curvature ◽

Harmonic Functions ◽

Minimal Graphs ◽

Curvature Estimates

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Curvature estimates for the level sets of spatial quasiconcave solutions to a class of parabolic equations

Science China Mathematics ◽

10.1007/s11425-011-4277-7 ◽

2011 ◽

Vol 54 (10) ◽

pp. 2063-2080 ◽

Author(s):

ChuanQiang Chen ◽

ShuJun Shi

Keyword(s):

Parabolic Equations ◽

Curvature Estimates

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The Convexity and the Gaussian Curvature Estimates for the Level Sets of Harmonic Functions on Convex Rings in Space Forms

Journal of Geometric Analysis ◽

10.1007/s12220-012-9339-8 ◽

2012 ◽

Vol 24 (1) ◽

pp. 337-374 ◽

Author(s):

Xi-Nan Ma ◽

Yongbing Zhang

Keyword(s):

Gaussian Curvature ◽

Harmonic Functions ◽

Space Forms ◽

Curvature Estimates

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