arXiv research

The paper establishes new band width inequalities for Riemannian bands.

Extends spectral torus band inequalities for compact manifolds with scalar curvature bounds.

Paper proves a noncompact version of Gromov's band-width estimate.

Study shows upper limit for torical band width with spectral curvature bounds.

Proves principles and estimates for initial data sets in Einstein equations.

The paper proves rigidity for certain product spaces and bounds for band widths.

Extends width estimates to family case using index theory.

The study refines known counterexamples in 4D to satisfy certain inequalities.

Study on Gehring link problem and width of bands in curved manifolds.

Establish optimal Lipschitz lower bounds for functions on manifolds with negative curvature, revealing interplay between width, boundary area, and topology.

The Rosenberg index vanishes if a manifold admits a wide Riemannian band or cube-like domain.

Estimates bandwidth for CMC initial data sets.

Develops connections between operator K-theory and positive scalar curvature.

We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal systolic in- equality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric…

Proves a quantitative index theorem for positive scalar curvature metrics.

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

The paper explores index theory for Dirac operators to understand scalar curvature properties.

The paper explores rigidity theorems for spectral curvature bounds in 3-manifolds.

Develops a robust hedging valuation adjustment measure for dynamic hedging under liquidity-demand stress.

Paper develops a robust HVA measure for dynamic hedging under liquidity stress.

This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.

Two lectures on metric geometry of manifolds.

Derives generalizations of the long neck principle and spectral width inequality.

The paper constructs optimal confidence bands for kernel gradient flow estimators.

The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.

Study shows torsion order bounds band-unlinking number for knot cobordisms.

A number of results for C$^2$-smooth surfaces of constant width in Euclidean 3-space ${\mathbb{E}}^3$ are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along…

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

The paper establishes a sub-additive inequality for volume and ε-phase-transition spectra of Riemannian manifolds.

UTOPIA aggregates multiple prediction intervals efficiently.

Sharp distance estimates for compact spin manifolds using Dirac operator.

In conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of d-band for imporved accuarcy) plays a central role in predicting adsorption energies and catalytic activity as a function of d-band center of the solid surfaces, but it requires density functional calculations that…

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $σ> 0$, the distance between the boundary components of $V$ is at most $C_n/\sqrtσ$, where $C_n = \…

Study shows limits on deep and shallow neural networks for approximating compact sets.

The paper bridges stochastic control and deep hedging for European call options with transaction costs.

Optimal constants for isoperimetric inequalities involving Steklov eigenvalues on surfaces are determined.

We give an analytical proof of the Poincare-type inequalities for widths of geodesic homotopies between equivariant maps valued in Hadamard metric spaces. As an application we obtain a linear bound for the length of an element conjugating two finite lists in a group acting on an Hadamard space.

The paper proves rigidity theorems for area widths of Riemannian manifolds.

The paper explores geometric relationships in manifolds with curvature constraints, proving new inequalities and rigidity results.

In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to $6$ and arbitrarily large widths. Our procedure is based on the connected sum construction of positive scalar curvature metrics due to Gromov and Lawson. We develop analogies between the area of…

The classical isoperimetric inequality in the Euclidean plane $\mathbb{R}^2$ states that for a simple closed curve $M$ of the length $L_{M}$, enclosing a region of the area $A_{M}$, one gets \begin{align*} L_{M}^2\geqslant 4πA_{M}. \end{align*} In this paper we present the improved isoperimetric inequality, which state…

Given a 2-dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M,g)=1 and every 1-cycle dividing M into two regions of equal area has length >C. It follows that there exists no universal inequality bounding 1-width of M in terms of its diameter. This answers a question of Ste…

Random groups prove length constraints on product of conjugates.

Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.

A new pricing controller handles resource constraints to infer target prices effectively.

The betting CI outperforms classical methods in constructing confidence intervals for bounded means.

For a null-homologous transverse link $\mathcal T$ in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect $δ(\mathcal T)$ of the Bennequin-Eliashberg inequality. We study relations between $δ(\mathcal T)$ and minimal genus Bennequin surface…

The volume spectrum of fiber bundles is bounded by the product of the base's volume spectrum and the fiber's volume.