arXiv research

Unique median structures found in hyperbolic spaces.

We prove that the natural $(\operatorname{Aff} _2(\mathbf{C}),\mathbf{C}^2)$-structure on an Inoue surface is the unique $(\operatorname{Bir}(\mathbb{P}^2),\mathbb{P}^2(\mathbf{C}))$-structure, generalizing a result of Bruno Klingler which asserts that the natural $(\operatorname{Aff}_2(\mathbf{C}),\mathbf{C}^2)$-struc…

Uniqueness proven for specific types of geometric structures.

We show uniqueness up to sign of positive, orthogonal almost-Kaehler structures on any non-scalar flat Kaehler-Einstein surface.

This paper proves unique determination of certain non-quasi-Fuchsian manifolds by their end structure and bending lamination.

Unique complex structures on specific Lie algebras.

Unique submaximal symmetry found for certain parabolic geometries.

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any 4-dimensional pseudo-Hermitian manifold also admits a unique Kaehler--Weyl stru…

Proves uniqueness and existence of toric gravitational instantons.

Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.

The paper addresses dynamic capital structure models with defaultable debt, proving existence and uniqueness.

Holomorphic structures on quantum flag manifolds uniquely defined.

New proof shows unique symplectic fillings for certain surface singularity links.

We define a new formal Riemannian metric on a conformal classes of four-manifolds in the context of the $σ_2$-Yamabe problem. Exploiting this new variational structure we show that solutions are unique unless the manifold is conformally equivalent to the round sphere.

Study proves all left-invariant contact structures on 3D Lie groups are tight.

In this paper we give a diameter bound for Sasaki manifolds with positive transverse Ricci curvature. As an application, we obtain the uniqueness of Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure.

We give an exposition of a theorem of Hirzebruch, Kodaira and Yau which proves the uniqueness of the Kahler structure of complex projective space, and of Yau's resolution of the Severi Conjecture.

This paper solves the structure of link concordance groups, proving they are infinitely generated.

Karigiannis discusses geometric flows of G2-structures, focusing on existence and uniqueness.

We prove that there is a unique real tight contact structure on the 3-ball with convex boundary up to isotopy through real tight contact structures. We also give a partial classification of the real tight solid tori with the real structure being antipodal map along longitudinal and the identity along meridional directi…

We will have a deep look at the set of all $G$-equivariant maps from the factor Lie group $G$ to the under the action manifold $M$, both from "computational" and "observability" viewpoint. We will also be looking for the existence of "unique" structure on this set, in a way that the induced-action of Lie group $G$ be s…

Researchers prove spectral uniqueness of complex/quaternionic structures on manifolds.

New metrics defined for full-rank correlation matrices, ensuring unique operations.

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kaehler covering W, with the deck transform acting on W by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its …

It is known that every ${\rm C}^r$-orbifold, $1\leq r\leq\infty$, has a compatible ${\rm C}^s$-differential structure, for every $s$, where $r< s\leqω$. We prove that if two reduced ${\rm C}^r$-orbifolds, $2\leq r\leqω$, are ${\rm C}^2$-diffeomorphic, then they are ${\rm C}^r$-diffeomorphic. It follows that the compati…

This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead the Kirby torus trick. This has the advantage of reducing the point-set topology …

Unique hyperbolic manifolds identified by boundary pleating.

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the local existence and uniqueness results which hold for genuine surfaces. Moreover…

In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provided that one of web foliations is pointed, there is also associated a unique affine struc…

In this paper, we prove that the transverse Mabuchi K-energy functional is convex along the weak geodesic in the space of Sasakian metrics. As an application, we obtain the uniqueness of constant scalar curvature Sasakian metrics modulo automorphisms for the transverse holomorphic structure.

Weyl-type theorems extended to Galilei and Carroll geometries.

Quillen connection links Riemann surfaces to projective structures.

Unique continuation property for measures in high dimensions.

Study shows unique linear equilibrium in market with constrained trader.

In this expository article, we illustrate how two independent flat structures on minimal surfaces induce a harmonic function, which captures the uniqueness of Enneper's surface.

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.

Paper studies Kähler-Ricci flow convergence on Fano manifolds.

We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…

Study on transverse knots and their neighborhoods, proving unique standard neighborhoods and destabilization results.

We introduce a flow of $G_2$-structures defining the same underlying Riemannian metric, whose stationary points are those structures with divergence-free torsion. We show short-time existence and uniqueness of the solution.

Introduces a new $G_2$-Hilbert functional in $G_2$-geometry.

Study on singularities in area-minimizing currents, proving unique tangent cones and rectifiability.

3-manifolds with toral boundary are uniquely determined by their profinite completions.

Study shows unique tangent cones for area-minimizing currents at boundary points.

Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.

We study the relation between an R-Cartan structure α and an (I, J, K)- generalized Finsler structure on a 3-manifold showing the difficulty in finding a general transformation that maps these structures each other. In some particular cases, the mapping can be uniquely determined by geometrical conditions.