arXiv research

Paper solves Minkowski problem for q-torsional rigidity using curvature flow.

Paper solves Minkowski problem for anisotropic p-torsional rigidity.

Paper solves Minkowski problem for k-torsional rigidity.

The paper examines torsional rigidity bounds under geometric flows.

This paper solves the dual Minkowski problem for q-torsional rigidity.

New method solves generalized Minkowski problem for torsional rigidity.

Paper introduces new $L_p$ $q$-torsional measure and solves Minkowski problem.

Study inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.

The study proves inequalities for eigenfunctions and torsional rigidity on curved spaces.

We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds P^m with controlled radial mean curvature in ambient Riemannian manifolds N^n with a pole p and with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsi…

We obtain upper bounds on the heat content and on the torsional rigidity of a complete Riemannian manifold M, assuming a generalized Hardy inequality for the Dirichlet Laplacian on M.

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs…

Projective structures are mostly rigid at the boundary but some are not.

Researchers find limits on curvature of certain 3D solitons.

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\niγ$-torsional rigidity $\mathcal{T}_{γ,\mathsf{g}}$ on a complete Riemannian two-manifold $(\mathbb M^2,\mathsf{g})$. Even in the special case of $\mathbb R^2$, major results …

Rigidity proven for a specific type of solitons with harmonic curvature.

Paper solves a new Minkowski problem for a specific type of rigidity.

This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.

New rigidity results for groups with specific properties.

We establish Bochner-type formulas for operators related to $CR$ automorphisms and spherical $CR$ structures. From such formulas, we draw conclusions about rigidity by making assumptions on the Tanaka-Webster curvature and torsion.

Classification of homogeneous almost complex 4-manifolds with non-degenerate torsion bundle

Paper studies how discrete space curves with constant torsion deform to model linkage motions.

Paper studies rigidity of translation surfaces in 3D sphere using quaternionic product.

Graphically discrete groups have strong rigidity properties.

Study graph products of groups, classifying them up to measure equivalence and rigidity.

Study on deformations of LC Spin(7) instantons simplifies the problem.

We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable abelian group of finite torsion free rank is coarsely equivalent to Z^n + H whe…

Classifies groups quasi-isometric to torsion-generated ones in specific hyperbolic groups.

Groups with certain properties have invariant subalgebra rigidity.

Proves a theorem on Alexander polynomials for 3-manifolds.

Flow solves $G_2$ system, proving existence of torsion-free metrics.

Study rigidity of PSU(1,1) actions on circle via harmonic measures.

The paper proves rigidity at infinity for specific lattices in Lie groups.

Let $\,(M,g)\,$ be a $n$-dimensional Riemannian manifold and $\,Ω\,$ be any compact connected domain in $\,M$. We study the problem of finding the {\em maxima} of the functional $\, {\mathcal E} (Ω)\,$ (known as {\em torsional rigidity} associated to $Ω$) among all domains of prescribed volume $v$. Our results show tha…

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this article, we…

Computes invariant for smooth h-cobordisms families, proving duality and vanishing theorems.

Study on scalar curvature deformations in pseudohermitian manifolds.

We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from the Euclidean $n$-space the following are equivalent: (1) order of growth of $π_1(N)$ is $n$, (2) $N$ is aspherical, and (3) $π_1(N)$ is virtually $\mathbb{Z}^n$ and torsion free.

The paper proves rigidity for cocycles from higher rank lattices to Out(FN).

New geometric approach to manifolds with density, proving rigidity results.

New proof shows homomorphisms from pure braid groups to hyperbolic groups have cyclic images or factor through forgetful maps.

Extended Regge complex for linearized Riemann-Cartan geometry and cohomology.

This article announces joint work with Frank Connolly and Jim Davis. We generalize our classification of pseudo-free involutions on the n-torus, by studying the action of the associated infinite group with torsion in the universal cover. Included is a non-Riemannian example obtained from the restriction of the action o…

Model proteins with bonds using Kauffman bracket skein module.

Study rank and torsion growth in higher rank lattices, proving vanishing invariants.

Study on compact strong HKT manifolds and their properties.

The study finds surface subgroups in specific types of groups.

Quantization and reduction studied for CR manifolds with group actions.