Given a Riemannian manifold M on a bounded domain endowed with the metric G, we construct a conformal change of the metric such that, for this new manifold, the distance from the boundary in the Riemannian metric coincides, in a neighbourhood of the boundary, with the distance from the boundary in the Euclidean case, thus inheriting its regularity properties as well.
The distance from the boundary in a Riemannian Manifold: Regularity up to a conformal change of the metric
Rondi L.
2021-01-01
Abstract
Given a Riemannian manifold M on a bounded domain endowed with the metric G, we construct a conformal change of the metric such that, for this new manifold, the distance from the boundary in the Riemannian metric coincides, in a neighbourhood of the boundary, with the distance from the boundary in the Euclidean case, thus inheriting its regularity properties as well.File in questo prodotto:
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