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Prof. Melanie Rupflin

Status
Academic Faculty
Contact form
+44 1865 615119
ORCID iD
https://orcid.org/0000-0002-9139-1400
Research groups
  • Oxford Centre for Nonlinear PDE

Address
Mathematical Institute
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.

Major / recent publications

Melanie Rupflin: Convergence of almost harmonic maps to geodesic bubble trees, arXiv:2210.13367

Melanie Rupflin: Lojasiewicz inequalities for almost harmonic maps near simple bubble trees, arXiv:2101.05527

Andrea Malchiodi, Melanie Rupflin, Ben Sharp:  Łojasiewicz inequalities near simple bubble trees

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

 
Preferred address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

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