We prove that the boundary of H-perimeter minimizing sets in the Heisenberg group can be approximated by graphs that are intrinsic Lipschitz. The Hausdorff measure of the symmetric difference in a ball of graph and boundary is estimated by excess in a larger concentric ball. This result is motivated by a research program on the regularity of H-perimeter minimizing sets.
Lipschitz approximation of H-perimeter minimizing boundaries
MONTI, ROBERTO
2014
Abstract
We prove that the boundary of H-perimeter minimizing sets in the Heisenberg group can be approximated by graphs that are intrinsic Lipschitz. The Hausdorff measure of the symmetric difference in a ball of graph and boundary is estimated by excess in a larger concentric ball. This result is motivated by a research program on the regularity of H-perimeter minimizing sets.
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