Status:
ORCID iD:
https://orcid.org/0000-0002-9139-1400
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
My main field of interest is geometric analysis, in particular the study of geometric flows
and problems related to harmonic maps and minimal surfaces.
Preferred address:
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Major / recent publications:
James Kohout, Melanie Rupflin, Peter M. Topping: Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow, arXiv:1909.06422
Craig Robertson, Melanie Rupflin: Finite-time degeneration for variants of Teichmüller harmonic map flow, arXiv:1807.06363
Melanie Rupflin: Hyperbolic metrics on surfaces with boundary, arXiv:1807.04464
Melanie Rupflin, Peter M. Topping: Global weak solutions of the Teichmüller harmonic map flow into general targets,
Anal. PDE 12 (2019), arXiv:1709.01881
Nadine Große, Melanie Rupflin: Holomorphic quadratic differentials dual to Fenchel-Nielsen coordinates,
Ann. Global Anal. Geom. 55 (2019), arXiv:1806.04384
Melanie Rupflin, Matthew R. I. Schrecker: Analysis of boundary bubbles for almost minimal cylinders,
Calc. Var. Partial Differential Equations 57 (2018), arXiv:1707.07985
Nadine Grosse and Melanie Rupflin: Sharp eigenvalue estimates on degenerating surfaces,
Comm. Partial Differential Equations 44 (2019), 573-612, arXiv:1701.08491
Melanie Rupflin and Peter M. Topping: Horizontal curves of hyperbolic metrics,
Calc. Var. PDE 57 (2018), arXiv:1605.06691
Reto Müller and Melanie Rupflin: Smooth long-time existence of Harmonic-Ricci Flow on surfaces, J. Lond. Math. Soc. 95 (2017), arXiv:1510.03643
Tobias Huxol, Melanie Rupflin, Peter M. Topping: Refined asymptotics of the Teichmüller harmonic map flow into general targets,
Calc. Var. PDEs 55 (2016), arXiv:1502.05791
Melanie Rupflin, Teichmüller harmonic map flow from cylinders,
Mathematische Annalen, 368 (2017), 1227-1276, arXiv:1501.07552
Melanie Rupflin, Oliver C. Schnürer: Weak solutions to mean curvature flow respecting obstacles, to appear in Ann. Sc. Norm. Super. Pisa, arXiv:1409.7529
Melanie Rupflin and Peter M. Topping: Teichmüller harmonic map flow into nonpositively curved targets,
J. Differential Geom. 108 (2018), arXiv:1403.3195
Melanie Rupflin and Peter M. Topping: A uniform Poincaré estimate for quadratic differentials on closed surfaces, Calc. Var. PDE 53 (2015), MR3347472
Melanie Rupflin, Peter M. Topping and Miaomiao Zhu: Asymptotics of the Teichmüller harmonic map flow, Adv. Math. 244 (2013), MR3115138
Melanie Rupflin: Flowing maps to minimal surfaces: Existence and uniqueness of solutions Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, MR3181674
Melanie Rupflin and Peter M. Topping: Flowing to minimal surfaces, American Journal of Mathematics
138 (2016), arXiv:1205.6298