arXiv research

Analyzes Saito vanishing theorem using $L^{2}$ methods.

The paper uses non-abelian Hodge theory to generalize Kodaira vanishing theorems.

Study on a knot invariant's vanishing order.

Proves a vanishing property for symplectic manifold cohomology.

Study on Nijenhuis tensor forms and vanishing properties.

New vanishing theorems for genera derived under almost nonnegative Ricci curvature.

A symplectic form has a primitive with nowhere vanishing $β$.

Generalizes Kodaira vanishing theorem to Kahler Lie algebroids.

Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing ideals plays a critical role. However, such an approximation also gives rise to a…

Only products of projective lines have vanishing Futaki invariants for all Kähler classes.

Study on harmonic Higgs bundles with vanishing endormorphism and eigenvalues of Q.

The non-vanishing conjecture implies the abundance conjecture in certain cases.

Paper discusses groups where twisted Alexander polynomials vanish.

The paper proves injectivity and vanishing theorems on compact Kahler manifolds.

The article studies cohomology on complex manifolds and proves vanishing theorems.

It is well known that the problem of vanishing/exploding gradients is a challenge when training deep networks. In this paper, we describe another phenomenon, called vanishing nodes, that also increases the difficulty of training deep neural networks. As the depth of a neural network increases, the network's hidden node…

New method identifies vanishing arcs for curve singularities.

The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designe…

Study pinched submanifolds, proving homology vanishing results.

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps fro…

In this paper, we will give a local version of the Hamilton-Ivey type pinching estimate of the gradient shrinking soliton with vanishing Weyl tensor, and then give a complete classification on gradient shrinking solitons with vanishing Weyl tensor.

Study cup products on CAT(0) cube complexes, proving quasimorphisms' vanishing results.

The study classifies metrics with vanishing curvature on complex manifolds.

Paper proves vanishing homology groups for certain hyperbolic groups.

Uniform criterion for vanishing products in bounded cohomology.

The paper supports a conjecture about a vanishing identity for certain 3-manifolds.

We prove the classical Nakano vanishing theorem with Hörmander $L^2$-estimates on a compact Kähler manifold using Siu's so called $\partial\dbar$-Bochner-Kodaira method, thereby avoiding the Kähler identities completely. We then introduce singular hermitian metrics on holomorphic vector bundles, and proceed to prove a …

We give several generalizations of the Kodaira vanishing and embedding theorems for Kähler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the embed…

Study virtual fundamental classes of derived manifolds, proving invariant vanishes.

Study Bochner formula on metric measure spaces for vanishing Betti numbers.

Paper extends rigidity and vanishing results for totally real submanifolds under $L^p$-integrable conditions.

We show vanishing theorems of $L^2$-cohomology groups of Kodaira-Nakano type on complete Hessian manifolds. We obtain further vanishing theorems of $L^2$-cohomology groups $L^2H^{p,q}(Ω)$ on a regular convex cone $Ω$ with the Cheng-Yau metric for $p>q$.

Study confirms optimal bounds for group cohomology of Lie groups.

In this article we find an upper and lower bound for the slope of genus g hyperelliptic Lefschetz fibrations, which is sharp when g = 2, and demonstrate the strong connection, in general, between the slope of hyperelliptic genus g Lefschetz fibrations and the number of separating vanishing cycles. Specifically, we show…

The paper studies Berwald scalar curvature properties in Finsler geometry.

New vanishing theorems for harmonic and pluriharmonic functions on Kähler and quaternionic Kähler manifolds.

Sigmoid-type networks avoid vanishing gradients with regularization and rescaling.

In this paper we give some sufficient conditions for the vanishing of the genus-2 G-function, which was introduced by B. Dubrovin, S. Liu and Y. Zhang in [DLZ]. As a corollary we prove their conjecture for the vanishing of the genus-2 G-function for ADE singularities.

Study $L^{2}$-harmonic forms on almost Kähler manifolds, extending vanishing theorems.

Study on Haantjes tensors for superintegrable systems, focusing on vanishing properties.

Defines a new knot invariant and studies its properties.

Proves a generalized vanishing theorem for quasi-smooth stacks, with applications in K-theory and birational geometry.

Vanishing theorem on CR manifolds with non-negative curvature.

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

Analyzes semi-characteristics on specific manifolds, proving a vanishing theorem.

Study cylindrical symmetric Finsler metrics with vanishing Douglas curvature.

We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statemen…

Study counts hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants up to volume $v$.