A method for the generation of quasi-isometric boundary-tted curvi-linear coordinates for arbitrary domains is developed on the basis of the quasi-isometric mappings theory and conformal representation of spherical and hyperbolic geometries. A one-parameter family of Riemannian metrics with some attractive invariant properties is analytically described. We construct the quasi-isometric mapping ...

Let (M, g) be an asymptotically hyperbolic manifold with a smooth conformal compactification. We establish a general correspondence between semilinear elliptic equations of scalar curvature type on ∂M and Weingarten foliations in some neighbourhood of infinity inM . We focus mostly on foliations where each leaf has constant mean curvature, though our results apply equally well to foliations whe...

The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N -dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained. The energies of the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian are calculated. The modified energy-momentum tensor with th...

Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization. However, for most of the state-of-the-art parameterization methods, the rank of the spline parameterization is usually large, which results in higher computatio...

We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. characterise surfaces such as either $S$-Willmore surfaces, quasi-umbilical constant mean curvature 3-dimensional space forms or lightlike lightcones. then investigate Bryant's quartic differential this context and show generically is dive...

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conform...

Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the...

A rigidity result for a class of compact generalized quasi-Einstein manifolds with constant scalar curvature is obtained. Moreover, under some geometric assumptions, the non-compact case also proved. Considering non curvature, we characterize which conformal to Euclidean space and show that there exist two classes complete manifolds, are obtained by considering potential functions factors eithe...

The Arnowitt–Deser–Misner (ADM) evolution equations for the induced metric and the extrinsic-curvature tensor of the spacelike surfaces which foliate the space-time manifold in canonical general relativity are a first-order system of quasi-linear partial differential equations, supplemented by the constraint equations. Such equations are here mapped into another first-order system. In particula...