arXiv research

The study establishes uncertainty principles on harmonic manifolds of rank one.

This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural appearence …

Researchers describe the metric structure of compact ECS manifolds.

New insights into compact rank-one ECS manifolds, proving they are bundles over circles.

We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly hyperbolic case and strengthens previous results by G. Knieper. We also establish s…

New random walk results on rank one symmetric spaces.

We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is a compact connected Lie group (simply connected in the quasi-Hamiltonian case). This work is a concretization of the more general classific…

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

Estimates the probability of a random symmetric tensor being close to rank-one.

Researchers compute the full spectrum of Laplace operator on distance spheres in symmetric spaces.

In this note we show that every (real or complex) vector bundle over a compact rank one symmetric space carries, after taking the Whitney sum with a trivial bundle of sufficiently large rank, a metric with nonnegative sectional curvature. We also examine the case of complex vector bundles over other manifolds, and give…

Extended Rank-One Theorem to special metric spaces.

In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Constructs explicit p-harmonic functions on specific Lie groups.

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for Hilbert geometries and characterize them as being equivalent to contracting elem…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary of the group. We show that equality is achieved precisely when the group stabili…

Classifies foliations on specific symmetric spaces.

We give a positive answer to the Chavel's conjecture [J. Diff. Geom. 4 (1970), 13-20]: a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is var…

New insights into Einstein hypersurfaces in symmetric spaces.

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

The aim of this paper is to study the spectrum of the $L^p$ Laplacian and the dynamics of the $L^p$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in t…

Study on estimating rank-one tensors in noisy data with heavy tails.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

Improved stability for matrix recovery from rank-one measurements.

Classifies rank-one submanifolds in Euclidean space.

No Einstein hypersurfaces found in Damek-Ricci spaces.

Improves graph-based active learning for non-Gaussian models.

Paper proposes a tensor model for clustering noisy multi-view data.

For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, we prove the existence of a canonical and functorial "intersection" connection on the Deligne pairing. A relationship is…

The study examines nilpotent similarity structures on manifolds and their properties.

First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the …

Compact rank one symmetric spaces are rigid under certain curvature conditions.

Study closed manifolds with rank one ray structures, proving completeness or covering properties.

In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.

We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.

Compact ECS manifolds have a simple topological structure.

We show that cocompact lattices in rank one simple Lie groups of non-compact type distinct from SO(2m,1) (m>0) contain surface subgroups.

Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank…

Novel algorithm for Markov decision processes using rank-one approximation.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter g…

We study the problem of existence of Kähler--Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree $22$ that admit a faithful action of the multiplicative group $\mathbb{C}^\ast$. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are Kähler--…

We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.

We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.

We formulate and solve a tensor model using a latent-variable approach.

The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.

The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.