Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Tinaglia, Giuseppe"'
Autor:
Tinaglia, Giuseppe, Zhou, Alex
In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimat
Externí odkaz:
http://arxiv.org/abs/2411.02151
We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that convergence always occurs with multiplicity one, which implies that the
Externí odkaz:
http://arxiv.org/abs/2102.02651
Publikováno v:
Geom. Topol. 26 (2022) 1849-1905
Democritus and the early atomists held that "the material cause of all things that exist is the coming together of atoms and void. Atoms are eternal and have many different shapes, and they can cluster together to create things that are perceivable.
Externí odkaz:
http://arxiv.org/abs/2006.16338
X.-J. Wang proved a series of remarkable results on the structure of convex ancient solutions to mean curvature flow. Some of his results do not appear to be widely known, however, possibly due to the technical nature of his arguments and his exploit
Externí odkaz:
http://arxiv.org/abs/1907.03932
We show that the only convex ancient solutions to curve shortening flow are the stationary lines, shrinking circles, Grim Reapers and Angenent ovals, completing the classification initiated by Daskalopoulos, Hamilton and Sesum and X.-J. Wang
Com
Com
Externí odkaz:
http://arxiv.org/abs/1903.02022
We prove, in all dimensions $n\geq 2$, that there exists a convex translator lying in a slab of width $\pi\sec\theta$ in $\mathbb{R}^{n+1}$ (and in no smaller slab) if and only if $\theta\in[0,\frac{\pi}{2}]$. We also obtain convexity and regularity
Externí odkaz:
http://arxiv.org/abs/1805.05173
We construct a compact, convex ancient solution of mean curvature flow in $\mathbb R^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it i
Externí odkaz:
http://arxiv.org/abs/1705.06981
Given a closed flat 3-torus $N$, for each $H>0$ and each non-negative integer $g$, we obtain area estimates for closed surfaces with genus $g$ and constant mean curvature $H$ embedded in $N$. This result contrasts with the theorem of Traizet [33], wh
Externí odkaz:
http://arxiv.org/abs/1611.05706
Publikováno v:
Math. Ann. 70 (2018) 1491-1512
For any $H$ in (0,1/2), we construct complete, non-proper, stable, simply-connected surfaces embedded in $H^2xR$ with constant mean curvature $H$.
Comment: Details added at referee's request. To appear in Mathematische Annalen
Comment: Details added at referee's request. To appear in Mathematische Annalen
Externí odkaz:
http://arxiv.org/abs/1609.08568
We derive intrinsic curvature and radius estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature and apply these estimates to study the global geometry of complete surfaces embedded in $\mathbb{R}^3$ with nonzero c
Externí odkaz:
http://arxiv.org/abs/1609.08032