3 papers
math.DG2023
Axially Symmetric Willmore Minimizers with Prescribed Isoperimetric Ratio
Jan-Henrik Metsch
We establish the existence and smoothness of minimizers of the Willmore energy among axially symmetric surfaces of spherical type with prescribed isoperimetric ratio. Afterwards, w…
math.AP2023
Parabolic and Elliptic Schauder Theory on Manifolds for a Fourth-Order Problem with a First- and a Third-Order Boundary Condition
Jan-Henrik Metsch
These notes provide a self-contained introduction to Schauder theory on manifolds. First, we derive Schauder estimates for a fourth-order parabolic linear problem with a first- and…
math.DG2023
On the Conditional Existence of Foliations by CMC and Willmore Type Half-Spheres
Jan-Henrik Metsch
We study half-spheres with small radii sitting on the boundary of a smooth bounded domain while meeting it orthogonally. Even though it is known that there exist families of CMC an…