Harmonic maps between flat surfaces with conical singularities.
Minimizing the Energy of Maps from a surface into a 2-shpere with prescribed degree and boundary values.
On solutions of the exterior Dirichlet problem for the minimal surface equation
Two-dimensional curvature functionals with superquadratic growth
For two-dimensional, immersed closed surfaces , we study the curvature functionals and with integrands and , respectively. Here is the second fundamental form, is the mean curvature and we assume . Our main result asserts that critical points are smooth in both cases. We also prove a compactness theorem for -bounded sequences. In the case of this is just Langer’s theorem [16], while for we have to impose a bound for the Willmore energy strictly below as an additional condition....
Embedded solutions for exterior minimal surface problems.
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