Gauss curvature estimates for the convex level sets of a minimal surface immersed in \(\mathbb R^{n+1}\)
DOI10.1016/j.na.2011.05.051zbMath1232.53052OpenAlexW1986231491MaRDI QIDQ555094
Publication date: 22 July 2011
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.na.2011.05.051
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms
- Principal curvature estimates for the level sets of harmonic functions and minimal graphs in \(\mathbb R^3\)
- On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes
- A constant rank theorem for level sets of immersed hypersurfaces in \(\mathbb R^{n+1}\) with prescribed mean curvature
- Principal curvature estimates for the convex level sets of semilinear elliptic equations
- Rearrangements and convexity of level sets in PDE
- Convexity of solutions of semilinear elliptic equations
- A maximum principle for sums of subharmonic functions, and the convexity of level sets
- Superharmonicity of curvatures for surfaces of constant mean curvature
- Capacitary functions in convex rings
- Convexity estimates for nonlinear elliptic equations and application to free boundary problems
- The concavity of the Gaussian curvature of the convex level sets of \(p\)-harmonic functions with respect to the height
- Curvature estimates in dimensions 2 and 3 for the level sets of $p$-harmonic functions in convex rings
- A Result Concerning Convex Level Surfaces of 3-Dimensional Harmonic Functions
- Quasiconcave solutions to elliptic problems in convex rings
- Gaussian curvature estimates for the convex level sets of p-harmonic functions
- Curvature of Level Curves of Harmonic Functions
- Note on the Green Function of a Star-Shaped Three Dimensional Region
- Convexity properties of solutions to some classical variational problems
- Conexity Of Level Sets For Solutions To elliptic Ring Problems
- On minimal surfaces bounded by two convex curves in parallel planes
- Notions of convexity
This page was built for publication: Gauss curvature estimates for the convex level sets of a minimal surface immersed in \(\mathbb R^{n+1}\)