• Corpus ID: 247450591

Curvature Varifolds with Orthogonal Boundary

  title={Curvature Varifolds with Orthogonal Boundary},
  author={Ernst Kuwert and Marius Muller},
We consider the class Sm ⊥ (Ω) of m-dimensional surfaces in Ω ⊂ Rn which intersect S = ∂Ω orthogonally along the boundary. A piece of an affine m-plane in Sm ⊥ (Ω) is called an orthogonal slice. We prove estimates for the area by the Lp-integral of the second fundamental form in three cases: first when Ω admits no orthogonal slices, second for m = p = 2 if all orthogonal slices are topological disks, and finally for all Ω if the surfaces are confined to a neighborhood of S. The orthogonality… 


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    Indiana University Mathematics Journal
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