46 citations · 83 across the 7 of their papers we have counts for
10 papers · 1 filter
Estimates for the Constant Mean Curvature Dirichlet Problem on Catenoids
Stephen J. Kleene
In this article, we solve the constant mean curvature dirichlet problem on catenoidal necks with small scale in $\mb{R}^3$. The solutions are found in exponentially weighted Hölder…
Minimal laminations with prescribed convex curvature blowup
Stephen J. Kleene
We construct minimal laminations with prescribed singularities on a line segment using perturbation techniques and PDE methods. In addition to the singular set, the rate of curvatu…
Non-compact families of complete, properly immersed minimal immersions with fixed topology via desingularization
Stephen J. Kleene, Niels Martin Moller
For fixed large genus, we construct families of complete immersed minimal surfaces in R3 with four ends and dihedral symmetries. The families exist for all large genus and at an ap…
Logarithmically spiraling helicoids
Christine Breiner, Stephen J. Kleene
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves…
A minimal lamination of the interior of a positive cone with quadratic curvature blowup
Christine Breiner, Stephen J. Kleene
We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.
Immersed self-shrinkers
Gregory Drugan, Stephen J. Kleene
We construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the to…