Radial Limits Determine Prescribed Mean Curvature Surfaces
The radial limits of a nonparametric prescribed mean curvature surface uniquely determine the surface.
math.AP↗
arXiv subjects
Alexandra K. Echart
Publications and source records attributed to Alexandra K. Echart.
A Generalization of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner"
The principle existence theorem (i.e. Theorem 1) of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner" (Pacific J. Math. Vol. 176, No. 1 (1996), 165-194) is extended to the case of a contact angle $γ$ which is not bounded away from $0$ and $π$ (and depends on position in a bounded domain $Ω\in {\bf R}^{2}$ with a convex corner at ${\cal O}=(0,0)$). The lower bound on the size of "side fans" (i.e. Theorem 2 in the above paper) is extended to case of such contact angles for convex and nonconvex corners.
math.AP↗
On Cusp Solutions to a Prescribed Mean Curvature Equation
The nonexistence of "cusp solutions" of prescribed mean curvature boundary value problems in $Ω\times{\bf R}$ when $Ω$ is a domain in ${\bf R}^{2}$ is proven in certain cases and an application to radial limits at a corner is mentioned.
math.AP↗