arXiv research

New groups with special properties found.

Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…

Study generalizes non-interaction theorems for relativistic systems.

We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and applied to the study of length 5 relations.

The paper proves drilled bundles over graphs are virtually special cubulable.

Revisits Finsler spacetimes from inertial observer perspective.

The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the proper time principle is introduced which makes it possible to devise experimenta…

Solves relative isoperimetric problem on polygonal domains, focusing on corners.

The paper proves rigidity properties of holomorphic isometries into homogeneous Kähler manifolds.

Study of portfolio management under relative performance concerns using mean field games.

The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If the tangent bundle is endowed also with a metric, it gives rise also to the not…

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relat…

We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of `V-stable' maps. Simple special cases include the Hurwitz nu…

We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector…

We shall construct a moduli space of pairs of Kähler-Einstein structures and special lagrangians and obtain smoothness of the moduli space of these pairs. Further we show that the moduli space of these pairs is locally embedded in a certain relative cohomology group.

Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given i…

We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth sp…

Study on deformations of special Lagrangians with boundary in Calabi-Yau manifolds.

This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized ruled …

Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.

We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective func…

There is no doubt that both the special and general theories of relativity capture the imagination. The anti-intuitive properties of the special theory of relativity and its deep philosophical implications, the bizzare and dazzling predictions of the general theory of relativity: the curvature of spacetime, the exotic …

This paper deals with relative normalizations of skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$. In section 2 we investigate some new formulae concerning the Pick invariant, the relative curvature, the relative mean curvature and the curvature of the relative metric of a relatively normalized ruled surface…

We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of discrepancy is given as follows. A curve of transformations in the special Eucli…

Following widely used in visual recognition concept of relative attributes, the article establishes definition of the relative PCA attributes for a class of objects defined by vectors of their parameters. A new rating model (RELARM) is built using relative PCA attribute ranking functions for rating object description a…

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively hyperbolic group structure and have one end. Applications include surface mapping clas…

For two complex vector bundles admitting a homomorphism, whose singularity locates in the disjoint union of some odd--dimensional spheres, we give a formula to compute the relative Chern characteristic number of these two complex vector bundles. In particular, for a spin manifold admitting some sphere bundle structure,…

We show how the Dixon's system of first order equations of motion for the particle with inner dipole structure together with the side Mathisson constraint follows from rather general construction of the 'Hamilton system' developed by Weyssenhoff, Rund and Grässer to describe the phase space counterpart of the evolution…

A surface $Σ\subset S^5 \subset \mathbb{C}^3$ is called \emph{special Legendrian} if the cone $0 \times Σ\subset \mathbb{C}^3$ is special Lagrangian. The purpose of this paper is to propose a general method toward constructing compact special Legendrian surfaces of high genus. It is proved \emph{there exists a compact,…

The Horikawa index and the local signature are introduced for relatively minimal fibered surfaces whose general fiber is a non-hyperelliptic curve of genus $4$ with unique trigonal structure.

We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…

Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other parts of Physics.

Random convolutional networks can be fooled with adversarial examples.

Study of skein invariants on tori for various groups and quantum parameters.

Unified geometry for relativity and beyond.

The study extends Dehn filling to Lie groups, ensuring geometric properties.

Kichenassamy's work spans theoretical physics, from relativity to applications.

Turning the skein relation for HOMFLY into a Fibonacci recurrence, we prove that there are only three rational specializations of HOMFLY polynomial: Alexander-Conway, Jones, and a new one. Using the recurrence relation, we find general and relative expansion formulae and rational generating functions for Alexander-Conw…

Let $X$ be a real-analytic manifold and $g\colon X\to{\mathbf R}^n$ a proper triangulable subanalytic map. Given a subanalytic $r$-form $ω$ on $X$ whose pull-back to every non singular fiber of $g$ is exact, we show tha $ω$ has a relative primitive: there is a subanalytic $(r-1)$-form $Ω$ such that $dgΛ(ω-dΩ)=0$. The p…

In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the growth rate of the group. In the proof, we study a special class of conical points …

Proves small cancellation free products have geometric actions on CAT(0) cube complexes.

The paper proposes and proves asymptotic expansions for quantum invariants.

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

Proof of local well-posedness for a specific boundary condition in general relativity.

The authors find geodesics, shortest arcs, diameter, cut locus, and conjugate sets for left-invariant sub-Riemannian metric on the Lie group SO(3), under condition that the metric is right-invariant relative to the Lie subgroup $SO(2)\subset SO(3)$.

For projective varieties with definite first Chern class we have one type of canonical metric which is called Kähler-Einstein metric. But for varieties with an intermidiate Kodaira dimension we can have several different types of canonical metrics. In this paper we introduce a new notion of canonical metric for varieti…

Study time-inconsistent portfolio optimization for competitive agents with relative performance criteria.

The paper discusses algorithms for reconstructing curves with given Euclidean or affine curvatures.