اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLocal convexity of renormalized volume for rank-1 cusped manifolds
255
0
0.0
(
0
)
تأليف
Franco Vargas Pallete
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 definition of the renormalized volume that is additive under gluing, and study some local properties.
قيم البحث
اقرأ أيضاً
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 $mathb
b{H}^3$. 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 $mathbb{H}^3$.
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 prove the existence of a periodic traveling wave of extreme form of the Whitham equation that has a convex profile between consecutive stagnation points, at which it is known to feature a cusp of exactly $C^{1/2}$ regularity. The convexity of Whit
hams highest cusped wave had been conjectured by Ehrnstrom and Wahlen.
We extend the concept of renormalized volume for geometrically finite hyperbolic $3$-manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic structures over an acylindrical 3-manifold $M$ with geometrically finite
limit. This allows us to show that the renormalized volume attains its minimum (in terms of the conformal class at $partial M = S$) at the geodesic class, the conformal class for which the boundary of the convex core is totally geodesic.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
