arXiv research

We prove generalized lower Ricci bounds for Euclidean and spherical cones over complete Riemannian manifolds. These cones are regarded as complete metric measure spaces. In general, they will be neither manifolds nor Alexandrov spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricc…

Unique minimal surfaces near quadratic cones are identified.

The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.

Researchers prove uniqueness of certain cylindrical tangent cones for special Lagrangians.

We prove generalized lower Ricci bounds for Euclidean and spherical cones over compact Riemannian manifolds. These cones are regarded as complete metric measure spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricci curvature is bounded from below by n-1 satisfies the curvature-di…

Paper constructs flows converging to cones and foliations.

In this paper we study the area minimizing problem in some kinds of conformal cones. This concept is a generalization of the cones in Eulcidean spaces and the cylinders in product manifolds. We define a non-closed-minimal (NCM) condition for bounded domains. Under this assumption and other necessary conditions we estab…

The study of Einstein manifolds with curvature operator cone conditions.

The study connects curvature operators' positivity to manifold topology.

Let C be a cone in the space of algebraic curvature tensors. Moreover, let (M,g) be a compact Einstein manifold with the property that the curvature tensor of (M,g) lies in the cone C at each point on M. We show that (M,g) has constant sectional curvature if the cone C satisfies certain structure conditions.

In the present paper we prove that, on a hyperkähler manifold, walls of the kähler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.

Study proves radial symmetry in convex cones using subharmonic functions.

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the unique compact, orientable, second order minima of the weighted area under variation…

The cone-volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition. As a consequence a conjectured (a dozen years ago) fundamental sharp affine isoperimetric inequality for the U-functional is completely established -- along with its equality conditions.

New Calabi-Yau metrics with conical singularities are created near complex lines.

Paper solves Dirichlet problem at infinity for Riemannian cones.

Study on sine-cones' spectra and stability under Ricci-de Turck flow.

Conditions for polyhedral Kähler metrics on CP^n with specific singularities.

New method classifies geodesics on cones.

Study inequalities for singular values of rectangular matrices.

Paper refines Einstein manifold result with cone curvature condition.

In the Batalin-Vilkovisky formalism, gauge conditions are expressed as Lagrangian submanifolds in the space of fields and antifields. We discuss a way of patching together gauge conditions over different parts of the space of fields, and apply this method to extend the light-cone gauge for the superparticle to a conic …

Study on cones over metric spaces with curvature bounds.

Study of geometric structures on projective space complement without Schwarz conditions.

The paper defines Vn-slant helices in a lightlike cone and their curvature functions.

The study finds conditions for area-minimizing cones over submanifolds.

Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.

We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As…

The paper proves conditions for existence of constant scalar curvature Kähler metrics with cone singularities.

Estimates solutions to Hessian quotient equations on HKT manifolds.

Paper constructs Thom-Smale complex using instantons from Morse functions.

Study coning totally geodesic boundaries of hyperbolic manifolds.

Proves approximation and interpolation for regular immersions directed by algebraically elliptic cones.

Study on minimizing singular capillary cones with stability and instability results.

This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary manifold is a convex cone and the flowing manifold is initially spacelike. Using a blowdown argument, we show that under renormalisation this flow converges toward…

Study hot spots on warped product manifolds and infinite cones.

Minimal cones defined by rank conditions in matrix spaces.

Study on $p$-Laplace equation in convex cones, proving rigidity under specific conditions.

Unique metric found for discrete curvature on spherical cone-metrics.

The paper explores cone structures and their connections to parabolic geometries in complex manifolds.

We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2π$, where the cone angles remain fixed or change in some smooth prescribed way. For the angle-preserving flow we prove long-time existence and convergence. When the Troyanov angl…

The study proves sub-Riemannian manifolds cannot satisfy $\mathrm{CD}$ conditions unless they are Riemannian.

Paper proves rigidity and index of Y-cones in unit ball.

Researchers compute the index of a specific operator on contact manifolds.

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles $>2π$. With an additional condition, we can weaken the requirement on one metric to `no conjugate points.'

The article studies factorization structures in geometry and their applications to cones and polytopes.

Establishes convexity and coercivity of K-energy functional for complex tori.

We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of $\mathbb{R}^n$. Our result applies to…