Marius Müller

activity

20202026

most citedThe Willmore Flow of Tori of Revolution

13 citations · 25 across the 9 of their papers we have counts for

collaborators

11 papers

math.AP2026

An Alt-Caffarelli problem for elastic graphs

Marius Müller

We study an Alt-Caffarelli-type free boundary problem for symmetric elastic graphs with fixed boundary height. Our results concern existence of minimizers and their description in…

math.DG2023

Short closed geodesics and the Willmore energy

Marius Müller, Fabian Rupp, Christian Scharrer

We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below $6 π$ . The energy threshold is optimal and the inequality cannot be extended to surfa…

math.AP2023

A biharmonic analogue of the Alt-Caffarelli problem

Hans-Christoph Grunau, Marius Müller

We study a natural biharmonic analogue of the classical Alt-Caffarelli problem, both under Dirichlet and under Navier boundary conditions. We show existence, basic properties and $…

math.AP2022

Polyharmonic equations involving surface measures

Marius Müller

This article studies (optimal) $W^{2 m - 1, \infty}$ -regularity for the polyharmonic equation $(- Δ)^{m} u = Q H^{n - 1} └ Γ$ , where $Γ$ is a (suitably regular) $(n - 1)$ …

math.AP2022★ 1 cited

On elliptic equations involving surface measures

Marius Müller

We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $- div (A (x) \nabla u) = Q H^{n - 1} └ Γ$ in a smooth do…

math.DG2022

Curvature Varifolds with Orthogonal Boundary

Ernst Kuwert, Marius Müller

We consider the class $S_{⊥}^{m} (Ω)$ of $m$ -dimensional surfaces in $Ω ˉ \subset R^{n}$ which intersect $S = \partial Ω$ orthogonally along the boundary. A piece of an af…

math.AP2022

An obstacle problem for the p-elastic energy

Anna Dall'Acqua, Marius Müller, Shinya Okabe +1

In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler--Lagrange equa…

math.AP2021★ 7 cited

Optimal thresholds for preserving embeddedness of elastic flows

Tatsuya Miura, Marius Müller, Fabian Rupp

We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. T…

math.DG2021★ 4 cited

A Li-Yau inequality for the 1-dimensional Willmore energy

Marius Müller, Fabian Rupp

By the classical Li-Yau inequality, an immersion of a closed surface in $R^{n}$ with Willmore energy below $8 π$ has to be embedded. We discuss analogous results for curves i…

math.AP2020

The elastic flow with obstacles: small obstacle results

Marius Müller

We consider a parabolic obstacle problem for Euler's elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacl…

math.AP2020★ 13 cited

The Willmore Flow of Tori of Revolution

Anna Dall'Acqua, Marius Müller, Reiner Schätzle +1

We study long-time existence and asymptotic behavior for the $L^{2}$ -gradient flow of the Willmore energy, under the condition that the initial datum is a torus of revolution. We sho…