A barrier principle at infinity for varifolds with bounded mean curvature
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866916090060210176 |
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| author | Gama, Eddygledson Souza de Lira, Jorge H. S. Mari, Luciano de Medeiros, Adriano A. |
| author_facet | Gama, Eddygledson Souza de Lira, Jorge H. S. Mari, Luciano de Medeiros, Adriano A. |
| contents | Our work investigates varifolds $Σ\subset M$ in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained in an open domain $Ω$. Under mild assumptions on the curvatures of $M$ and on $\partial Ω$, also allowing for certain singularities of $\partial Ω$, we prove a barrier principle at infinity, namely we show that the distance of $Σ$ to $\partial Ω$ is attained on $\partial Σ$. Our theorem is a consequence of sharp maximum principles at infinity on varifolds, of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08946 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A barrier principle at infinity for varifolds with bounded mean curvature Gama, Eddygledson Souza de Lira, Jorge H. S. Mari, Luciano de Medeiros, Adriano A. Differential Geometry Analysis of PDEs Our work investigates varifolds $Σ\subset M$ in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained in an open domain $Ω$. Under mild assumptions on the curvatures of $M$ and on $\partial Ω$, also allowing for certain singularities of $\partial Ω$, we prove a barrier principle at infinity, namely we show that the distance of $Σ$ to $\partial Ω$ is attained on $\partial Σ$. Our theorem is a consequence of sharp maximum principles at infinity on varifolds, of independent interest. |
| title | A barrier principle at infinity for varifolds with bounded mean curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2004.08946 |