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9 papers · 2 filters
Properly embedded minimal planar domains with infinite topology are Riemann minimal examples
William H. Meeks, Joaquin Perez
These notes outline recent developments in classical minimal surface theory that are essential in classifying the properly embedded minimal planar domains M in R^3 with infinite to…
A note on the p-Parabolicity of Submanifolds
Ana Hurtado, Vicente Palmer
We give a geometric criterion which shows p-parabolicity of a class of submanifolds in a Riemannian manifold, with controlled second fundamental form, for p bigger or equal than 2.
A new proof of a characterization of small spherical caps
Rafael López
It is known that planar disks and small spherical caps are the only constant mean curvature graphs whose boundary is a round circle. Usually, the proof invokes the Maximum Principl…
Proper harmonic maps from hyperbolic Riemann surfaces into the Euclidean plane
Antonio Alarcon, Jose A. Galvez
Let be a compact Riemann surface and a finite number of pairwise disjoint closed disks of . We prove the existence of a proper harmonic map into the Euclidean…
Complete Flat Surfaces with two Isolated Singularities in Hyperbolic 3-space
Armando V. Corro, Antonio Martinez, Francisco Milan
We construct examples of flat surfaces in which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in with only o…
Existence of proper minimal surfaces of arbitrary topological type
Leonor Ferrer, Francisco Martin, William H. Meeks
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immers…