arXiv research

Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Sc…

The paper calculates extreme measures in continuous time conic finance.

New measures found in 3-uniform geometry.

Study examines wave equation decay and Strichartz estimates on conic manifolds.

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

New formulations for comparing metric measure spaces with arbitrary positive measures.

Given a coassociative 4-fold N with a conical singularity in a varphi-closed 7-manifold M (a manifold endowed with a distinguished closed 3-form varphi), we construct a smooth family, {N'(t): t\in(0,tau)} for some tau>0, of (smooth, nonsingular,) compact coassociative 4-folds in M which converge to N in the sense of cu…

For a torsion free Kleinian group $Γ$ without parabolics, we consider the decomposition of the limit set $L(Γ)$ into conical and ending limit sets and compare the Patterson-Sullivan measure with the harmonic measure on $L(Γ)$ when $L(Γ)=S^2_\infty$.

In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowl…

The study connects Hilbert entropy to non-differentiability points of limit sets in flag spaces.

A new algorithm solves sparse optimization problems on measures efficiently.

New algorithm minimizes Bayesian regret in offline linear bandits.

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…

The paper classifies isoparametric hypersurfaces in conic Finsler spaces.

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

Study conic singular manifolds, proving Lipschitz normal embedding.

The abstract discusses maximal rank 4-webs formed by confocal conics and their properties.

Desingularizes conically singular Cayley submanifolds.

Modified flow smooths conical Kähler-Ricci problem.

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.

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

Proves conic version of YTD conjecture on log Fano manifolds.

Paper identifies conditions for singularity removal in equations with conical singularities.

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

Study Schauder estimates for conical singularities using Kähler metrics.

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.

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

Study constant Q-curvature metrics on conic 4-manifolds.

Study describes ALF instantons with conical singularities.

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

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…

The paper discusses a twisted conical Kähler-Ricci flow and its convergence properties.

Study conical Ricci flow on surfaces with explicit asymptotic expansions.

The study proves convergence of conic 4-spheres' geometry to boundary cases.

Generalized Gauss-Bonnet formula for conical metrics on compact Riemann surfaces.

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

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

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

Constructs surfaces with conical singularities using variational methods.

Study shows scalar curvature rate for conical Kähler-Ricci flow near singularity.

Paper proves unique conical tangent flows in all dimensions.

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

The Yamabe flow preserves conical singularities under certain conditions.