CPAA
Principal curvature estimates for the level sets of harmonic functions and minimal graphs in $R^3$
Xi-Nan Ma Jiang Ye Yun-Hua Ye
Communications on Pure & Applied Analysis 2011, 10(1): 225-243 doi: 10.3934/cpaa.2011.10.225
We give a sharp lower bound for the principal curvature of the level sets of harmonic functions and minimal graphs defined on convex rings in $R^3$ with homogeneous Dirichlet boundary conditions.
keywords: level sets minimal graph. harmonic function Curvature estimate
DCDS
Principal curvature estimates for the convex level sets of semilinear elliptic equations
Sun-Yung Alice Chang Xi-Nan Ma Paul Yang
Discrete & Continuous Dynamical Systems - A 2010, 28(3): 1151-1164 doi: 10.3934/dcds.2010.28.1151
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary gradient. We also extend this result to a class of semi-linear elliptic partial differential equations under certain structure condition.
keywords: semilinear elliptic equation. Curvature estimate level sets

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