Critical Allard regularity: pointwise tilt-excess estimates
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913237585362944 |
|---|---|
| author | McCurdy, Sean |
| author_facet | McCurdy, Sean |
| contents | The main results of this paper provide VMO-type estimates for the quadratic tilt-excess on varifolds with critical generalized mean curvature. These estimates apply to varifolds with "almost-integral" density which are close to a multiplicity one $m$-disc in a ball in the usual senses. The class of almost-integral varifolds allows for varifolds with non-perpendicular mean curvature. Moreover, the estimates hold \emph{uniformly for every point} in a relatively open set in $\text{spt}||V||$ and naturally imply a Reifenberg-type parametrization. The proof relies upon generalizing the $Q$-valued Lipschitz approximation and Sobolev-Poincaré estimates of arXiv:0808.3660 to almost-integral rectifiable varifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical Allard regularity: pointwise tilt-excess estimates McCurdy, Sean Differential Geometry 49Q15 (Primary) The main results of this paper provide VMO-type estimates for the quadratic tilt-excess on varifolds with critical generalized mean curvature. These estimates apply to varifolds with "almost-integral" density which are close to a multiplicity one $m$-disc in a ball in the usual senses. The class of almost-integral varifolds allows for varifolds with non-perpendicular mean curvature. Moreover, the estimates hold \emph{uniformly for every point} in a relatively open set in $\text{spt}||V||$ and naturally imply a Reifenberg-type parametrization. The proof relies upon generalizing the $Q$-valued Lipschitz approximation and Sobolev-Poincaré estimates of arXiv:0808.3660 to almost-integral rectifiable varifolds. |
| title | Critical Allard regularity: pointwise tilt-excess estimates |
| topic | Differential Geometry 49Q15 (Primary) |
| url | https://arxiv.org/abs/2402.12752 |