2 citations · 3 across the 6 of their papers we have counts for
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The umbilic set of Willmore surfaces
Reiner M. Schätzle
It is well known that the umbilic points of minimal surfaces in spaces of constant sectional curvature consist only of isolated points unless the surface is totally umbilic on some…
Conformal Willmore Tori in
Tobias Lamm, Reiner M. Schätzle
For every two-dimensional torus and every , , we construct a conformal Willmore immersion with exactly one point of density $…
Control of the isoperimetric deficit by the Willmore deficit
Matthias Röger, Reiner Schätzle
In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit can be controlled by the Willmore deficit.
Minimizers of the Willmore functional under fixed conformal class
Ernst Kuwert, Reiner Schätzle
We consider the problem of minimizing the Willmore energy in the class of conformal immersions of a given closed, genus p Riemann surface into R^n for n=3,4. We prove existence of…
Closed surfaces with bounds on their Willmore energy
Ernst Kuwert, Reiner Schätzle
The Willmore energy of a closed surface in R^n is the integral of its squared mean curvature, and is invariant uner Möbius transformations of R^n. We show that any torus in R^3 wit…