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math.AP2026
Regular Curves, Singular Graphs: Cantor Parts and the Relaxed Willmore Energy
Hans-Christoph Grunau, Boris Gulyak
One might expect that finite relaxed elastic energy rules out diffuse singularities in the derivative, leaving only absolutely continuous and jump parts. This is suggested by the r…
math.AP2026
The Willmore Flow of Graphs with Boundary Data: Low-Regularity Initial Data and Global Convergence
Boris Gulyak
We study the Willmore flow for graphs over a bounded domain in with Dirichlet (clamped) boundary conditions, a still little-studied setting that also serves as a pro…
math.AP2025
Graphical Willmore Problems with Low-Regularity Boundary and Dirichlet Data
Boris Gulyak
We establish existence and regularity results for boundary value problems arising from the first variation of the Willmore energy in the graphical setting. Our focus lies on two-di…