Research Interests:

• Higher order free boundary problems (Obstacle-type and Alt-Caffarelli-type)
• Higher order gradient flows with obstacle constraint
• Geometric evolution equations for the Elastic/Willmore energy
• Elastic Curves and Elastic Flow of Curves in Space Forms
• Anisotropic Curvature and the Anisotropic Willmore Energy

Publications and Preprints:

• A. Dall'Acqua, M.Müller, R.Schätzle, A.Spener. The Willmore Flow of Tori of Revolution (Preprint 2020)
• M.Müller. The Biharmonic Alt-Caffarelli Problem in 2D (Preprint 2020)
• M.Müller.  On Gradient Flows with Obstacles and Euler's Elastica. Nonlinear Anal. 192 (2020).
• M.Müller, A. Spener. On the Convergence of the Elastic Flow in the Hyperbolic Plane. Geom. Flows (2020)
• An obstacle problem for elastic curves: existence results. Interfaces Free Bound. 21 (2019), no. 1, 87–129.

Academic Talks:

• Nov 25, 2019: Winter School 'Gradient Flows and Variational Methods in PDE's', Ulm University,  "On Gradient Flows with Obstacles"
• Jul 30, 2019: TULKKA-Treffen, KIT Karlsruhe, "The biharmonic Alt-Caffarelli Problem".
• Dec 13, 2018: Weekly Seminar, EDDY Research Training Group, RWTH Aachen, "On Gradient Flows with Obstacles and Euler's Elastica".

• A biharmonic Bernoulli problem
• Elasticae in the hyperbolic plane

Betreute Veranstaltungen:

• SoSe 2020: Riemannsche Geometrie
• WiSe 2019/2020: Advanced Topics in the Calculus of Variations
• SoSe 2018: Elementare Differenzialgeometrie
• WiSe 2017/18: Variationsrechnung
• SoSe 2017: Elemente der Funktionentheorie
• SoSe 2017: Elemente der Funktionalanalysis