| A mean curvature flow arising in adversarial training
with Leon Bungert and Kerrek Stinson,
to appear in J. Math. Pures Appl., 32 pp. | https://arxiv.org/abs/2404.14402 | |
| Quantitative convergence of the nonlocal Allen-Cahn equation to volume-preserving mean curvature flow,
with Milan Krömer,
to appear in Math. Ann., 14 pp. | https://arxiv.org/abs/2309.12409 | |
| Generic level sets in mean curvature flow are BV solutions,
with Anton Ullrich,
to appear in J. Geom. Anal., 16 pp. | https://arxiv.org/abs/2301.01097 | |
| Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow,
with Kerrek Stinson and Clemens Ullrich,
European J. Appl. Math. (first view) 61 pp. | https://arxiv.org/abs/2212.11939 | |
| A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,
with Sebastian Hensel,
to appear in J. Differential Geom., 38 pp. | https://arxiv.org/abs/2109.04233 | |
| The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions,
with Julian Fischer, Sebastian Hensel, and Theresa M. Simon,
first part to appear in J. Eur. Math. Soc. (JEMS), 104 pp. | https://arxiv.org/abs/2003.05478 | |
| Large data limit of the MBO scheme for data clustering: Convergence of the dynamics,
with Jona Lelmi,
J. Mach. Learn. Res. (JMLR) 24(344):1-49, 2023 | https://jmlr.org/papers/v24/22-1089.html | |
| A phase-field version of the Faber-Krahn theorem,
with Paul Hüttl and Patrik Knopf,
to appear in Interfaces Free Bound., 30 pp. | https://arxiv.org/abs/2207.10946 | |
| Sharp interface limit of the Cahn-Hilliard reaction model for lithium-ion batteries,
with Kerrek Stinson,
Math. Models Methods Appl. Sci., 33:12, 2557–2585, 2023. | https://doi.org/10.1142/S0218202523500550 | |
| Phase-field methods for spectral shape and topology optimization,
with Harald Garcke, Paul Hüttl, Christian Kahle, and Patrik Knopf,
ESAIM: Control Optim. Calc. Var. 29:10, 57 pp., 2023. | https://doi.org/10.1051/cocv/2022090 | |
| Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets,
with Jakob Fuchs,
Adv. Calc. Var. (online first), 59 pp. | https://doi.org/10.1515/acv-2022-0020 | |
| Weak-strong uniqueness for volume-preserving mean curvature flow,
Rev. Mat. Iberoam. 40:1, pp. 93–110, 2024. | https://ems.press/journals/rmi/articles/8082294 | |
| The Hele-Shaw flow as the sharp interface limit of the Cahn-Hilliard equation with disparate mobilities,
with Milan Krömer,
Comm. Partial Differential Equations, 47(12):2444-2486, 2022. | https://www.tandfonline.com/doi/full/10.1080/03605302.2022.2129384 | |
| BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness, with Sebastian Hensel, Indiana Univ. Math. J. ( http://www.iumj.indiana.edu/IUMJ/Preprints/9701.pdf ), 24 pp. | https://arxiv.org/abs/2112.11150 | |
| Weak-strong uniqueness for the mean curvature flow of double bubbles,
with Sebastian Hensel,
Interfaces Free Bound. 25, no. 1, pp. 37–107, 2023. | https://doi.org/10.4171/ifb/484 | |
| De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions,
with Jona Lelmi,
Calc. Var. Partial Differential Equations, 61(1):35, 42 pp., 2022. | https://link.springer.com/article/10.1007/s00526-021-02146-8 | |
| Nematic-isotropic phase transition in liquid crystals: A variational derivation of effective geometric motions,
with Yuning Liu,
Arch. Ration. Mech. Anal. 241(3):1785-1814, 2021. | https://link.springer.com/article/10.1007/s00205-021-01681-0 | |
| Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,
with Julian Fischer and Theresa M. Simon,
SIAM J. Math. Anal., 52(6):6222-6233, 2020. | https://epubs.siam.org/doi/abs/10.1137/20M1322182?af=R&mobileUi=0 | |
| Mullins-Sekerka as the Wasserstein flow of the perimeter,
with Antonin Chambolle,
Proc. Amer. Math. Soc., 149(7):2943-2956, 2021. | https://www.ams.org/journals/proc/2021-149-07/S0002-9939-2021-15401-4/ | |
| Implicit time discretization for the mean curvature flow of mean convex sets,
with Guido De Philippis,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 21:911-930, 2020. | https://journals.sns.it/index.php/annaliscienze/article/view/924 | |
| Well-posedness for degenerate elliptic PDE arising in optimal learning strategies,
with J. Miguel Villas-Boas,
Interfaces Free Bound., 22(1):119-129, 2020. | https://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=22&iss=1&rank=5 | |
| Brakke's inequality for the thresholding scheme,
with Felix Otto,
Calc. Var. Partial Differential Equations, 59(1):39, 26 pp., 2020. | https://link.springer.com/content/pdf/10.1007/s00526-020-1696-8.pdf | |
| Analysis of diffusion generated motion for mean curvature flow in codimension two: A gradient-flow approach,
with Aaron Yip,
Arch. Ration. Mech. Anal., 232(2):1113-1163, 2019. | http://link.springer.com/article/10.1007/s00205-018-01340-x | |
| Convergence of the Allen-Cahn equation to multiphase mean curvature flow,
with Theresa M. Simon,
Comm. Pure Appl. Math., 71(8):1597-1647, 2018. | http://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21747 | |
| Gradient-flow techniques for the analysis of numerical schemes for multi-phase mean-curvature flow,
Geometric Flows, 3(1):76-89, 2018. | http://www.degruyter.com/view/j/geofl.2018.3.issue-1/geofl-2018-0006/geofl-2018-0006.xml | |
| The elastic flow of curves on the sphere,
with Anna Dall'Acqua, Chun-Chi Lin, Paola Pozzi, and Adrian Spener,
Geometric Flows, 3(1):1-13, 2018. | http://www.degruyter.com/view/j/geofl.2018.3.issue-1/geofl-2018-0001/geofl-2018-0001.xml | |
| Convergence of thresholding schemes incorporating bulk effects,
with Drew Swartz,
Interfaces Free Bound., 19(2):273-304, 2017. | http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=19&iss=2&rank=5 | |
| Convergence of the thresholding scheme for multi-phase mean-curvature flow,
with Felix Otto,
Calc. Var. Partial Differential Equations, 55(5):129, 74 pp., 2016. | http://link.springer.com/article/10.1007%2Fs00526-016-1053-0 | |
