Removability of point singularities of Willmore surfaces

By Ernst Kuwert, R. Schatzle. 2004

265 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7cd914d3708efb4d356d01c112dd49e577935154

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Computation of geometric partial differential equations and mean curvature flow (2005, methodology): “They were subsequently able to remove the smallness assumption and to prove the existence of a global smooth solution provided that E(X0) ≤ 16π, where Γ0 = X0(S2) (see Kuwert and Schätzle (2004b) and note that our definition differs from theirs by a factor of 2).”
$W^{2,2}$-conformal immersions of a closed Riemann surface into $\R^n$ (2010, background): “) ≤ C(γ) Z D |A|2 dµg +kukL1(D) . 2.2 Simon’s monotonicity formula We brieﬂy review the monotonicity identity from [S] for proper W2,2 conformal immersions f : Σ → Rn. For more details we refer to [K-S1]. Since f is locally Lipschitz, the measure µ= f(µg) is an integral varifold with multiplicity f”
Analysis aspects of Willmore surfaces (2008, methodology): “Finally, combining again arguments in [ KS3 ] (pages 350-351) together with our point removability result and a theorem by Montiel in [Mon] which in particular implies that any non-umbillic Willmore 2-spheres in R 4 has Willmore energy larger than 8π (this was known in R 3 since the work of Bryant [”
Error analysis of a finite element method for the Willmore flow of graphs (2006, background): “DZIUK solution provided that W(f0) 6 16π , whereΓ0 = f0(S(2)) (see [12] and note that our definition differs from the one used in [12] by a factor of 2).”
Geometric flows with rough initial data (2009, background): “In the case that Σ is a sphere Kuwert & Schätzle [13]-[15] showed that if W (f0) ≤ 8π, then the Willmore flow exists for all times and subconverges to a smooth Willmore sphere.”
Min-Max theory and the Willmore conjecture (2012, methodology): “This can be used to produce a continuous function fi : R(i) → T such that fi(x) = |Φ(x, 1/2)| on ∂R(i).”
Willmore Minimizers with Prescribed Isoperimetric Ratio (2011, background): “For the part concerning the Willmore flow see [10].”
The Wulff shape minimizes an anisotropic Willmore functional (2004, background): “Furthermore, these experiments show that the result obtained in [9] is optimal.”
The Willmore Conjecture (2014, background): “extends the analysis of point singularities of [28] to the higher codimension case.”
A level set formulation for Willmore flow (2004, background): “In [21] [23] they are able to prove convergence to round spheres unter suitable assumptions on the initial surface.”
Variational Principles for immersed Surfaces with $L^2$-bounded Second Fundamental Form (2010, background): “The Li–Yau inequality (see [15]), which also holds for varifolds with weak L(2)-bounded mean curvature which are smooth outside one point (as proved in [13]), implies”