arXiv research

Study of how small changes in triangulated surfaces affect their geometry.

We extend to the conformal realm the concept of genuine deformations of submanifolds, introduced by Dajczer and the first author for the isometric case. Analogously to that case, we call a conformal deformation of a submanifold $M^n$ genuine if no open subset of $M^n$ can be included as a submanifold of a higher dimens…

Study finds conditions for conformal deformations to constant scalar curvature in conic metrics.

Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.

The paper classifies hypersurfaces with specific conformal deformations.

The paper explores how to increase Steklov spectral gaps on manifolds with fixed boundary.

We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.

We address the problem of second order conformal deformation of spacelike surfaces in compactified Minkowski 4-space. We explain the construction of the exterior differential system of conformal deformations and discuss its general and singular solutions. In particular, we show that isothermic surfaces are singular sol…

Study on conformal deformations of complex Finsler metrics.

Paper constructs new non-Anosov Partially Hyperbolic Geodesic flows using conformal deformations.

CAT(0) spaces can be deformed in various ways.

The paper solves scalar curvature problems under conformal deformation for Riemannian manifolds.

We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly from C^0 estimates for fully nonlinear equations. The main result has appeared i…

New metrics connect surfaces with Anosov flows to those with negative curvature.

The paper solves a problem in 3D geometry about conformally deforming metrics.

In this paper we expose on the dual 1-jet space J^{1*}(R,M^4) the distinguished (d-) Riemannian geometry (in the sense of d-connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) for the (t,x)-conformal deformed Berwald-Moor Hamiltonian metric of order four.

The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) attached to the (t,x)-conformal deformation of the Berwald-Moor metric.

Smooth Riemannian manifolds can be embedded without boundary.

Compact metrics from singular conformal deformations with curvature bounds.

The paper proves uniformization for specific curvature types on manifolds.

Study concavity of solutions to elliptic equations under conformal deformations.

Proves a Schwarz-type lemma for noncompact manifolds with boundary.

Study curvatures on compact pseudo-Hermitian manifolds using special methods.

The paper studies curvature changes on manifolds with boundary.

The paper proves properties of minimal isometric embeddings and conformal deformations of Riemannian surfaces.

This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.

We consider the problem of conformally deforming a metric to one with a prescribed symmetric function of the eigenvalues of the Ricci tensor, in the case of negative curvature.

Study on stability of α-harmonic maps and their applications.

Study on curvature functions for compact manifolds with boundary.

The abstract discusses metrics with positive biorthogonal curvature on 5-manifolds.

In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schrödingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one with suitable presumptions. As applications, we investigated compactly conformal defo…

Researchers prove spaces of positive scalar curvature metrics are contractible with symmetry.

Conditions for scalar curvature on compact manifolds under conformal deformation.

The paper solves curvature prescription on a disk with negative Gaussian curvature.

In this paper, we investigate the prescribed scalar curvature problem on a non-compact Riemannian manifold $(M, \langle \, , \, \rangle)$, namely the existence of a conformal deformation of the metric $\langle \, , \, \rangle$ realizing a given function $\widetilde s(x)$ as its scalar curvature. In particular, the work…

The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.

Study Bernstein-Gelfand-Gelfand complexes on Lipschitz domains, computing cohomology and applying to elasticity models.

On pseudo-Riemannian manifolds of even dimension $n\geq 4$, with everywhere vanishing (Fefferman-Graham) obstruction tensor, we construct a complex of conformally invariant differential operators. The complex controls the infinitesimal deformations of obstruction-flat structures, and, in the case of Riemannian signatur…

The study finds multiple solutions to a complex metric problem using bifurcation theory.

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.

In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is non-negative definite.

Study on metrics with positive scalar curvature and convex boundary.

Study on Hausdorff dimension of singular CR Yamabe problem.

Consider a geometrically finite Kleinian group $G$ without parabolic or elliptic elements, with its Kleinian manifold $M=(\H^3\cup Ω_G)/G$. Suppose that for each boundary component of $M$, either a maximal and connected measured lamination in the Masur domain or a marked conformal structure is given. In this setting, w…

The paper simulates Lévy processes and their extremum and hitting time.

Let $(M,g)$ be a compact connected orientable Riemannian manifold of dimension $n\ge4$ and let $λ_{k,p} (g)$ be the $k$-th positive eigenvalue of the Laplacian $Δ_{g,p}=dd^*+d^*d$ acting on differential forms of degree $p$ on $M$. We prove that the metric $g$ can be conformally deformed to a metric $g'$, having the sam…

A metric with positive sectional curvature on the Gromoll-Meyer exotic 7-sphere is constructed explicitly. The proof relies on a 2-parameter family of left invariant metrics on Sp(2) and a one-parameter family of conformal deformations via an isoparametric function F on it. One byproduct is a metric with positive secti…

In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization to higher dimensions of the well known Riemann mapping Theorem in the plane.