اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCombinatorial Ricci flow on cusped 3-manifolds
83
0
0.0
(
0
)
تأليف
Xu Xu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Combinatorial Ricci flow on a cusped $3$-manifold is an analogue of Chow-Luos combinatorial Ricci flow on surfaces and Luos combinatorial Ricci flow on compact $3$-manifolds with boundary for finding complete hyperbolic metrics on cusped $3$-manifolds. Dual to Casson and Rivins program of maximizing the volume of angle structures, combinatorial Ricci flow finds the complete hyperbolic metric on a cusped $3$-manifold by minimizing the co-volume of decorated hyperbolic polyhedral metrics. The combinatorial Ricci flow may develop singularities. We overcome this difficulty by extending the flow through the potential singularities using Luo-Yangs extension. It is shown that the existence of a complete hyperbolic metric on a cusped $3$-manifold is equivalent to the convergence of the extended combinatorial Ricci flow, which gives a new characterization of existence of a complete hyperbolic metric on a cusped $3$-manifold dual to Casson and Rivins program. The extended combinatorial Ricci flow also provides an effective algorithm for finding complete hyperbolic metrics on cusped $3$-manifolds.
قيم البحث
اقرأ أيضاً
Combinatorial Ricci flow on an ideally triangulated compact 3-manifold with boundary was introduced by Luo as a 3-dimensional analog of Chow-Luos combinatorial Ricci flow on a triangulated surface and conjectured to find algorithmically the complete
hyperbolic metric on the compact 3-manifold with totally geodesic boundary. In this paper, we prove Luos conjecture affirmatively by extending the combinatorial Ricci flow through the singularities of the flow if the ideally triangulated compact 3-manifold with boundary admits such a metric.
We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabais theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to sphe
rical space forms other than $S^3$ and $RP^3$ and hyperbolic manifolds, to prove that the moduli space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold $X$, the inclusion $text{Isom} (X,g)to text{Diff}(X)$ is a homotopy equivalence for any Riemannian metric $g$ of constant sectional curvature.
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The
novelty of the approach is we rely heavily on the naturality of binary symmetric groups to avoid lengthy explicit constructions of smoothings of PL-manifolds.
Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies and generalizes Chow-Luos combinatorial Ricci flow for Thurstons circ
le packings, Luos combinatorial Yamabe flow for vertex scaling and the combinatorial Calabi flow for discrete conformal structures on surfaces. For Thurstons Euclidean and hyperbolic circle packings on triangulated surfaces, we prove the longtime existence and global convergence of the fractional combinatorial Calabi flow. For vertex scalings on polyhedral surfaces, we do surgery on the fractional combinatorial Calabi flow by edge flipping under the Delaunay condition to handle the potential singularities along the flow. Using the discrete conformal theory established by Gu et al., we prove the longtime existence and global convergence of the fractional combinatorial Calabi flow with surgery.
This paper studies the combinatorial Yamabe flow on hyperbolic surfaces with boundary. It is proved by applying a variational principle that the length of boundary components is uniquely determined by the combinatorial conformal factor. The combinato
rial Yamabe flow is a gradient flow of a concave function. The long time behavior of the flow and the geometric meaning is investigated.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
