arXiv research

Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.

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

Constructs surfaces with conical singularities using variational methods.

Optimal family of Calabi-Yau cone metrics found for toric Kähler cones.

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…

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

New conic quadratic formulations improve outlier detection in regression models.

Study finds equivalence between MMV and MV preferences with conic constraints.

Defines Perelman's functionals on manifolds with non-isolated conical singularities.

SOC-ICNN expands neural network representational capacity by using conic optimization.

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…

We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function of [Busseti et al., 2018], the problem solution map is differentiabl…

The paper classifies isoparametric hypersurfaces in conic Finsler spaces.

Two unique conic-line arrangements with degree 9 are found.

Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.

Study conic singular manifolds, proving Lipschitz normal embedding.

Mathematical analysis shows Delisle-Euler map methods are optimal.

New framework solves low-rank optimization problems to certifiable optimality.

Desingularizes conically singular Cayley submanifolds.

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

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

The study computes indicial roots and metric convergence orders for Ricci-flat conifolds.

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies …

Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, 3) the net of tangents to a conic of the confocal family…

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

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 $k$ …

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…

Proves smoothness of conical singularities in mean curvature flow.

This paper introduces a new formulation of the Conic Gromov-Wasserstein distance for comparing complex network structures.

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

Study describes ALF instantons with conical singularities.

We establish a parabolic version of Tian's $C^{2,α}$-estimate for conical complex Monge-Ampere equations, which includes conical Kähler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical Kähler-Ricci flow in arXiv:1411.7284.

We prove that the conical Kähler-Ricci flows introduced in \cite{CYW} exist for all time $t\in [0,+\infty)$. These immortal flows possess maximal regularity in the conical category. As an application, we show if the twisted first Chern class $C_{1,β}$ is negative or zero, the corresponding conical Kähler-Ricci flows co…

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…

Study conic-line arrangements of degree 7, finding their topology and components.

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

The paper explores conic-line arrangements via Poncelet's theorem and finds families of reducible curves.

Paper proves unique conical tangent flows in all dimensions.

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

Paper shows regularizing flow for conical Kähler-Ricci equations.

FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.

Study curve shortening flow on Riemann surfaces with conic singularities.

Proves positive mass theorem on conical manifolds with small angles.

We discuss the constant $σ_{2}$ problem for conic 4-spheres. Based on earlier works of Chang-Han-Yang and Han-Li-Teixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp, we have the uniqueness result similar to that of Troyanov in dimension 2. It indicat…

The paper classifies Landsberg metrics on a 2D Lie group and proves a conjecture.

The abstract proves spherical surface decompositions with conical singularities.

Paper proves Whitney stratified spaces can be given a conically smooth structure.

The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.