On a Modified Conjecture of De Giorgi

By Matthias Röger, R. Schatzle. 2006

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A general regularity theory for weak mean curvature flow (2011, methodology): “We mention that a simple proof of [19, 33] was obtained by Sato [29] utilizing the result of Röger-Schätzle [27] (see also [28]) for k = n − 1 and n = 2, 3.”
A new phase-field model for strongly anisotropic systems (2009, methodology): “…construct phase-field approximations for the Willmore energy date back to De Giorgi (1991), who conjectured an appropriate approximation, which has since been analysed and simplified using different methods by Loreti & March (2000), Du et al. (2004, 2005), Röger & Schätzle (2006) and Wang (2007).”
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications (2011, methodology): “Ω 1 ε ∣∣∣∣ε∆u− 1εf(u) ∣∣∣∣2 Γ− converges to 2σ‖κ‖2L2(Γ)? The latter question was answered positively (under the additional conditions that Eε(uε) ≤ C) by Röger and Schätzle [39] in dimensions 2 and 3.”
Second Order Rectifiability of Integral Varifolds of Locally Bounded First Variation (2008, methodology): “Results of the type obtained in the present paper have proven useful, for example, in the context of Brakke’s mean curvature flow, or sharp and diffuse interfaces, or image reconstruction, or the Willmore functional; see [7, 9, 26, 28–30, 32] and the references therein.”