Surfaces of bounded mean curvature in Riemannian manifolds
| dc.creator | Gadgil, Siddartha | |
| dc.creator | Seshadri, Harish | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:40Z | |
| dc.date.available | 2026-07-07T10:17:40Z | |
| dc.description | Consider a sequence of closed, orientable surfaces of fixed genus $g$ in a Riemannian manifold $M$ with uniform upper bounds on mean curvature and area. We show that on passing to a subsequence and choosing appropriate parametrisations, the inclusion maps converge in $C^0$ to a map from a surface of genus $g$ to $M$. We also show that, on passing to a further subsequence, the distance functions corresponding to pullback metrics converge to a pseudo-metric of fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface $F\subset M$ together with bounds on the geometry of $M$ give an upper bound on the diameter of $F$. Our proof is modelled on Gromov's compactness theorem for $J$-holomorphic curves. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0811.1820 | |
| dc.identifier | http://arxiv.org/abs/0811.1820 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173929 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21 | |
| dc.title | Surfaces of bounded mean curvature in Riemannian manifolds | |
| dc.type | text |