3 papers
math.AP2026
Weighted estimates for the stability operator of the helicoid on slowly varying domains
Stephen J. Kleene
We consider the poisson problem $\wt{\mc{L}} u = E$ for the operator $\wt{\mc{L}} = Δ_{\mb{R}^2} + 2\cosh^{-2}(s)$ on domains of the form , whe…
math.AP2026
A Decay Estimate For The Stability Operator Of The Helicoid
Stephen J. Kleene
We consider the Poisson Problem for the stability operator of the helicoid on a vertical strip, under the assumption that the source term is supported on a strip of fixed height. W…
math.DG2023
Constant Mean Curvature surfaces with prescribed finite topologies
Stephen. J. Kleene
In this article, we construct complete embedded constant mean curvature surfaces in $\mb{R}^3$ with freely prescribed genus and any number of ends greater than or equal to four. He…