arXiv research

Study on Hausdorff dimension of boundaries of relatively hyperbolic groups.

Based on C. Li and Y. Rubinstein's upper bisectional curvature bound estimate for the conic Kähler metric, we can construct a smoothing sequence for the conic metric with uniformly upper bisectional curvature bound. For the conic metric along a simple normal crossing divisor with triple or higher multiple points we may…

The paper discusses polynomial convergence to conical Kähler-Einstein metrics.

Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.

The paper defines conic reach and shows polynomial parallel volume in the plane.

The paper shows how to stabilize perturbed Kähler-Ricci solitons.

Generically, topological insulators have conical points leading to Dirac-like currents.

Proves conditions for positive scalar curvature on certain manifolds with conical singularities.

As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing long-time existence, and in particular the fact that the flow preser…

Study spherical surfaces with conical points, proving systole inequality.

Study on mean curvature flow of graphs in higher dimensions.

A limit point p of a discrete group of Mobius transformations acting on S^n is called a concentration point if for any sufficiently small connected open neighborhood U of p, the set of translates of U contains a local basis for the topology of S^n at p. For the case of Fuchsian groups (n = 1), every concentration point…

The paper pinches curvature in expanding Ricci solitons.

The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics are its critical points. Finally we proved the convexity of the coni…

Proves existence of Yamabe metrics on conical manifolds with conical points and links.

Study finds determinant of Laplacian on a special surface with a conical point.

Finite number of metrics found for specific spherical angles.

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points. Dynamical properties for the space of geodesics are also proved.

Uniform elliptic theory for Dirac operators on orbifold resolutions.

We study the asymptotics of the determinant of Laplacian on a translation surface (a compact Riemann surface equipped with a conformal flat conical metric with trivial holonomy) of genus g with 2g-2 conical points of angle 4πas two conical points collide.

The study creates Kähler-Einstein metrics with conical singularities.

Proves existence of Yamabe metrics on conical 4-manifolds using min-max method.

Study X-ray transform on conic spaces, proving injectivity under certain conditions.

Study on spherical conical metrics and their reducibility on compact Riemann surfaces.

We study metrics on conic 2-spheres when no Einstein metrics exist. In particular, when the curvature of a conic metric is positive, we obtain the best curvature pinching constant. We also show that when this best pinching constant is approached, the conic 2-sphere has an explicit Gromov-Hausdorff limit. This is a gene…

In this paper we develop a systematic deformation theory for conic constant curvature metrics on a closed surface when all cone angles are less than $2π$; in particular, we define and study the Teichmüller space $\mathcal{T}^{\mathrm{conic}}_{γ,k}$ of conic constant curvature metrics on a surface of genus $γ$ with $k$ …

We compute the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the resulting groups turn out to be big.

Study curve shortening flow on Riemann surfaces with conical singularities.

Study Ricci flow on spaces with conical singularities, proving existence and curvature estimates.

Given a hyperbolic subgroup $H$ of a hyperbolic group $G$ for which a Cannon-Thurston map $\hat i:\partial H \ra \partial G$ exists, we study the limit set $Λ_H$ of $H$ with respect to its action on $\partial G$. We prove that the set of conical limit points is exactly the subset of $Λ_H$ consisting of the points to wh…

Researchers find necessary conditions for conic 4-spheres with constant σ₂ metrics.

Study the determinant of Laplacians on Riemann surfaces with conical metrics.

Study conical Ricci flow on surfaces with explicit asymptotic expansions.

Proves smoothness of conical singularities in mean curvature flow.

Study heat trace expansion on manifolds with conic points.

Gradient flow solves curvature problem on surfaces with conical points.

The paper studies the topology of spherical tori with one conical point.

Characterizes conical angles for metrics with dihedral symmetry.

Conic singular sub-manifolds are Lipschitz Normally Embedded in compact non-Euclidean manifolds.

The article completes the research of two-point G$^2$ Hermite interpolation problem with spirals by inversion of conics. A simple algorithm is proposed to construct a family of 4th degree rational spirals, matching given G$^2$ Hermite data. A possibility to reduce the degree to cubic is discussed.

Study metrics with conical singularities on Riemann surfaces, deriving determinant formulas.

We list all the possible fundamental groups of the complements of real conic-line arrangements with two conics which are tangent to each other at two points, with up to two additional lines. For the computations we use the topological local braid monodromies and the techniques of Moishezon-Teicher and van-Kampen. We al…

Paper proposes a method to find approximate SOSP for nonconvex conic optimization problems.

The Kähler-Ricci flow near conical singularities is described with a $C/t$ curvature bound.

The flow contracts cone divisors on Kähler surfaces to points.

We show that spheres of positive constant curvature with $n$ ($n\geq3$) conic points converge to a sphere of positive constant curvature with two conic points (or called an (American) football) in Gromov-Hausdorff topology when the corresponding singular divisors converge to a critical divisor in the sense of Troyanov.…

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.

Paper proposes a method to find approximate SOSP for nonconvex conic optimization problems.