Research Interests
Research Interests
My research interests lie in geometric analysis, partial differential equations, and the calculus of variations, often with connections to biomechanics and elasticity.
My research interests lie in geometric analysis, partial differential equations, and the calculus of variations, often with connections to biomechanics and elasticity.
In particular, these include the following topics:
Bending energies and their applications (e.g., Willmore functional, elastic curves, Canham–Helfrich model):
Existence theory (inhomogeneous materials, obstacle problems, free boundaries)
Regularity (multiplicity control, varifolds)
Geometric evolution equations (e.g., Willmore flow, elastic flow, mean curvature flow):
Asymptotic behavior (global existence, Łojasiewicz–Simon inequalities)
Analysis of singularities (blow-up analysis, classification)
Properties preserved by higher-order equations (embeddedness, graphicality)
Geometry of submanifolds:
Closed geodesics
Calibrated geometry and minimal surfaces
[19] T. Miura, F. Rupp. Calibration energy and mean curvature flow (2026). [arXiv]
[18] A. Dall'Acqua, F. Rupp, R. Schätzle, M. Schlierf. Stability of the free boundary Willmore problem (2026). [arXiv]
[17] T. Miura, F. Rupp. Embeddedness and graphicality of the elastic flow for complete curves (2025). [arXiv]
[16] M. Röger, F. Rupp. Elastic bilayer membranes under confinement - Existence, regularity, and rigidity (2025). [arXiv]
[15] T. Miura, F. Rupp. A new energy method for shortening and straightening complete curves. J. Reine Angew. Math., vol. 2026, no. 830 (2026) pp. 1-50. [arXiv] [journal]
[14] A. Dall'Acqua, M. Müller, F. Rupp, M. Schlierf. Dimension reduction for Willmore flows of tori: fixed conformal class and analysis of singularities (2025). [arXiv]
[13] F. Rupp, C. Scharrer, M. Schlierf. Gradient flow dynamics for cell membranes in the Canham-Helfrich model. Arch. Ration. Mech. Anal. 250, 81 (2026). [arXiv] [journal]
[12] F. Rupp, C. Scharrer. Global regularity of integral 2-varifolds with square integrable mean curvature. J. Math. Pures Appl. 204, 103797 (2025). [arXiv] [journal]
[11] A. Dall'Acqua, G. Jankowiak, L. Langer, F. Rupp. Conservation, convergence, and computation for evolving heterogeneous elastic wires. SIAM J. Math. Anal. 56:4 (2024), 4494-4529. [arXiv] [journal]
[10] K. Brazda, M. Kružík, F. Rupp, U. Stefanelli. Curvature-dependent Eulerian interfaces in elastic solids. Philos. Trans. Roy. Soc. A. 381, (2263) (2023) . [arXiv] [journal]
[9] M. Müller, F. Rupp, C. Scharrer. Short closed geodesics and the Willmore energy. J. Differential Geom. 132 (2026), no. 3, 429-459. [arXiv] [journal]
[8] A. Dall'Acqua, L. Langer, F. Rupp. A dynamic approach to heterogeneous elastic wires. J. Differential Equations 392 (2024), 1-42. [arXiv] [journal]
[7] F. Rupp, C. Scharrer. Li–Yau inequalities for the Helfrich functional and applications. Calc. Var. Partial Differential Equations 62, 45 (2023). [arXiv] [journal]
[6] T. Miura, M. Müller, F. Rupp. Optimal thresholds for preserving embeddedness of elastic flows. Amer. J. Math. 147 (2025), no. 1, 33--80. [arXiv] [journal]
[5] F. Rupp. The Willmore flow with prescribed isoperimetric ratio. Comm. Partial Differential Equations 49:1-2 (2024), 148-184. [arXiv] [journal]
[4] M. Müller, F. Rupp. A Li-Yau inequality for the 1-dimensional Willmore energy. Adv. Calc. Var. 16 (2023), no. 2, 337–362. [arXiv] [journal]
[3] F. Rupp. The volume-preserving Willmore flow. Nonlinear Anal. 230 (2023), 113220. [arXiv] [journal]
[2] F. Rupp, A. Spener. Existence and convergence of the length-preserving elastic flow of clamped curves. J. Evol. Equ. 24, 59 (2024). [arXiv] [journal]
[1] F. Rupp. On the Lojasiewicz-Simon gradient inequality on submanifolds. J. Funct. Anal. 279 (2020), 108708. [arXiv] [journal]
[T] F. Rupp. Constrained gradient flows for Willmore-type functionals. PhD thesis (2022). [published version]