In this paper, we introduce a practical modeling approach to improve the quality of polygonal mesh structures. Our approach is based on a discrete version of Gaussian-Bonnet theorem on piecewise planar manifold meshes and vertex angle deflections that determines local geometric behavior. Based on discrete GaussianBonnet theorem, summation of angle deflections of all vertices is independent of m...

The purpose of this article is to explain how pseudo-holomorphic curves in a symplectic 4-manifold can be constructed from solutions to the Seiberg-Witten equations. As such, the main theorem proved here (Theorem 1.3) is an existence theorem for pseudo-holomorphic curves. This article thus provides a proof of roughly half of the main theorem in the announcement [T1]. That theorem, Theorem 4.1, ...

A. Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Outπ1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel’s theorem holds for a compact Lie group G acting ...

A hypoelliptic operator in the Heisenberg calculus on a compact contact manifold is Fredholm operator. Its symbol determines an element K-theory of noncommutative algebra symbols. We construct periodic cyclic cocycle which, when paired with Connes-Chern character principal symbol, calculates index. Our index formula local, i.e. given as local expression terms and connection TM its curvature. pr...

We study a codimension two steady-state/steady-state mode interaction with D4 symmetry, where the center manifold is three-dimensional. Primary branches of equilibria undergo secondary Hopf bifurcations to periodic solutions which undergo further bifurcations leading to chaotic dynamics. This is not an exponentially small effect, and the chaos obtained in simulations using DsTool is large-scale...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators ‘acting on sections of the bundle’ in a formal sense. In particular any oriented even-dimensional manifold carries a projective spin Dirac operator in this sense. More generally the corresponding space of pseudodiffere...

We will generalize Jaco’s Handle Addition Theorem to the ncompressibility of surfaces on the boundary of 3-manifolds. Several corollaries are given, which show how the theorem can be applied to different situations. 1 The Handle Addition Theorem was first proved by Przytycki [6] in the case when M is a handlebody. In [4] Jaco proved the general version below. Handle Addition Theorem [4] Suppose...

Abstract We prove a normal form for contact forms close to Zoll one and deduce that on any closed manifold are local maximizers of the systolic ratio. Corollaries this result are: (1) sharp inequalities Riemannian Finsler metrics ones, (2) perturbative case conjecture Viterbo symplectic capacity convex bodies, (3) generalization Gromov’s non-squeezing theorem in intermediate dimensions symplect...

Abstract This article studies a nonlinear parabolic equation on complete weighted manifold where the metric and potential evolve under super Perelman-Ricci flow. It derives elliptic gradient estimates of local global types for positive solutions exploits some their implications notably to general Liouville type theorem, Harnack inequalities classes Hamilton dimension-free estimates. Some exampl...