اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIsoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds
144
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We reinterpret the renormalized volume as the asymptotic difference of the isoperimetric profiles for convex co-compact hyperbolic 3-manifolds. By similar techniques we also prove a sharp Minkowski inequality for horospherically convex sets in $mathbb{H}^3$. Finally, we include the classification of stable constant mean curvature surfaces in regions bounded by two geodesic planes in $mathbb{H}^3$ or in cyclic quotients of $mathbb{H}^3$.
قيم البحث
اقرأ أيضاً
In this article we show that for any given Riemann surface $Sigma$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $Sigma$ in terms of the genus and the combined
extremal lengths on $Sigma$ of $(g-1)$ disjoint, non-homotopic, simple closed compressible curves. This result is used to partially answer a question posed by Maldacena about comparing renormalized volumes of Schottky and Fuchsian manifolds with the same conformal boundary.
We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate
notion of limit. This result generalizes previous work in the subject.
We study global aspects of the mean curvature flow of non-separating hypersurfaces $S$ in closed manifolds. For instance, if $S$ has non-vanishing mean curvature, we show its level set flow converges smoothly towards an embedded minimal hypersurface
$Gamma$. We prove a similar result for the flow with surgery in dimension 2. As an application we show the existence of monotone incompressible isotopies in manifolds with negative curvature. Combining this result with min-max theory, we show that quasi-Fuchsian and hyperbolic $3$-manifolds fibered over $mathrm{S}^1$ admit smooth entire foliations whose leaves are either minimal or have non-vanishing mean curvature. We also conclude the existence of outermost minimal surfaces for quasi-Fuchsian ends and study their continuity with respect to variations of the quasi-Fuchsian metric.
We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a modified d
efinition of the renormalized volume that is additive under gluing, and study some local properties.
In this paper we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoper
imetric inequality, in terms of their Gromov boundary improving similar results from a previous work. In particular, we prove that having a pole is a necessary condition and, therefore, it can be removed as hypothesis.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
