arXiv research

New CR almost Schur Lemma estimates curvature on compact manifolds.

In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,θ)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $θ$ is pseudo-Einstein and the pseudo-Hermitian scalar curvature is constant.

The paper proves new curvature estimates in quaternionic contact geometry.

In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X. Cheng and De Lellis-Topping whenever the weighted function f is constant.

Researchers prove a stability result for a 3-sphere inequality, extending previous work.

Paper extends Schur's theorem to spherical curves via monotonicity.

Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\Rico:=\Ric-\frac{R}{n}g$$ is identically zero. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci …

In our previous paper in \cite{C}, we generalized the almost-Schur lemma of De Lellis and Topping for closed manifolds with nonnegative Rcci curvature to any closed manifolds. In this paper, we generalize the above results to symmetric $(2,0)$-tensors and give the applications including $r$th mean curvatures of closed …

Deep neural networks are proven universally powerful using Koopman operator.

In this short note we establish an integral geometric inequality in a smooth metric measure space of the nonnegative Bakry-Émery Ricci curvature. This result can be regarded as a mild generalization of the almost Schur theorem due to De Lellis and Topping (Calc. Var., DOI: 10.1007/s00526-011-0413-z).

After shortly recalling the construction of the Khovanov-Kuperberg algebras, we give a characterisation of indecomposable web-modules. It says that a web-module is indecomposable if and only if one can deduce it directly from the Kuperberg bracket (via a Schur lemma argument). The proofs relies on the construction of i…

Quantifies Schur's theorem for curves in CAT(k) spaces.

An $η$-Einstein condition is introduced in the context of indefinite g.f.f-manifolds, and a few Schur-type lemmas for indefinite S-manifolds are provided.

Characterizes submanifolds with minimum ratio of diameter to focal radius.

Proves estimate similar to De Lellis-Müller on Minkowski lightcone.

Paper studies curvature in Finsler geometry, proving curvature constancy under isotropy.

Paper derives a Reilly type integral formula and applies it to inequalities and eigenvalue problems.

In this article, we define a symmetric 2-tensor canonically associated to Q-curvature called J-tensor on any Riemannian manifold with dimension at least three. The relation between J-tensor and Q-curvature is precisely like Ricci tensor and scalar curvature. Thus it can be interpreted as a higher-order analogue of Ricc…

Our main goal in this work is to deal with results concern to the $σ_2$-curvature. First we find a symmetric 2-tensor canonically associated to the $σ_2$-curvature and we present an Almost Schur Type Lemma. Using this tensor we introduce the notion of $σ_2$-singular space and under a certain hypothesis we prove a rigid…

Paper proves a new volume comparison theorem for Riemannian manifolds.

The paper defines new types of positivity and proves properties of Schur forms for vector bundles.

Based on a self-contained, coordinate-free exposition of the necessary concepts and tools of spray and Finsler geometry (with detailed proofs), we derive new results among others on the consequences of the direction-independence of the Landsberg tensor and the stretch tensor of a Finsler manifold. We show that an at le…

In this article, we first establish the main tool - an integral formula for Riemannian manifolds with multiple boundary components (or without boundary). This formula generalizes Reilly's original formula from \cite{Re2} and the recent result from \cite{QX}. It provides a robust tool for sub-static manifolds regardless…

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem (in the large) in Alexandrov geometry.

Proves a formula for Kontsevich-Witten tau-function using Schur Q-polynomials.

We show that the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$ is $\mathbb Z/2\mathbb Z$, when $D$ is divisible by 4.

New unoriented versions of Schur and Bogomolov multipliers for finite groups.

Let X=G/P be cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) We say a Schubert class [S] is Schur rigid if the only irreducible subvarieties Y of X with homology class [Y] = r [S], for an integer r, are Schubert varieties. Robles and The identifie…

Efficiently computes embeddings for large graphs using coarsening.

Schur theorem proven for weakly Landsberg Finsler metrics.

New basis and Schur-Weyl duality for loop Hecke algebra defined.

New method connects neural networks to diagrammatic algebra.

Study framizations of algebras using Schur--Weyl duality and tied braids.

Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n…

A new method for efficient portfolio optimization using graph structures.

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then this curvature is a global constant.

The paper studies connectivity of Schur-Horn map images in real Grassmannians.

We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples.

Defines odd Khovanov homology via categorification of q-Schur algebra.

It was recently shown by R. Souam and E. Toubiana that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by perturbative arguments, that all analytic metrics sufficiently close to the round metric $g_{0}$ on $\mathbb{S}^{3}$ possess \textsl{general…

New gauge invariants from framed 3-manifolds match Hopf algebra indicators.

Constructs new topological theories in 2D not fitting standard axioms.

Method for conditional sampling with pre-trained normalizing flows.

New algorithm learns ReLU networks efficiently using Schur polynomials.

The paper finds new inequalities for convex polygons.

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the…

Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.

The paper proves positivity of characteristic forms for certain vector bundles.