arXiv research

Study on Nijenhuis tensor forms and vanishing properties.

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

Proves a vanishing property for symplectic manifold cohomology.

Study pinched submanifolds, proving homology vanishing results.

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

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…

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

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…

Uniform criterion for vanishing products in bounded cohomology.

New rigidity results for tensors on non-compact manifolds with curvature conditions.

In this paper we find sufficient conditions for the vanishing of the Morse-Novikov cohomology on Riemannian foliations. We work out a Bochner technique for twisted cohomological complexes, obtaining corresponding vanishing results. Also, we generalize for our setting vanishing results from the case of closed Riemannian…

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

Study proves Witten genera vanish for certain manifolds, supporting a conjecture.

We prove the non-vanishing of the CMC flux of the boundaries of certain Riemannian manifolds with constant mean curvature.

The paper studies Berwald scalar curvature properties in Finsler geometry.

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

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

Study confirms optimal bounds for group cohomology of Lie groups.

In this short note we update a result proved in [16]. This will complete our program of [12] showing that the structure set vanishes for compact aspherical 3-manifolds.

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

The paper introduces Lagrangian vanishing cycles to prove obstructions for symplectic foliations.

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

Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $Γ$ of orientation-preserving isometries acts freely, so that the quotient $X=M/Γ$ is compact. We prove a vanishing theorem for a half-kernel of a $Γ$-invariant Dirac operator on a $Γ$-equivariant Clifford module over $M$, twisted by …

Kawakubo and Uchida showed that, if a closed oriented $4k$-dimensional manifold $M$ admits a semi-free circle action such that the dimension of the fixed point set is less than $2k$, then the signature of $M$ vanishes. In this note, by using $G$-signature theorem and the rigidity of the signature operator, we generaliz…

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

Study on a knot invariant's vanishing order.

Study vanishing theorems for CR manifolds using contact forms and Laplacian formulas.

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for Stiefel-Whitney numbers of (finite co…

In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in $L^2$.

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are given.

New result on group actions in CAT(0) spaces with vanishing escape rate.

We prove a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions. This extends a previous result of Ziran Liu who proves it for the case where the acting group is unimodular.

The paper proves vanishing theorems for harmonic forms and spinors on stable minimal hypersurfaces.

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

New expressions for Nijenhuis tensor squares found.

When $X=Γ\backslash \H^n$ is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of $L^2$ harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.

We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain some vanishing results for $\hat A$-type genera.

The paper proves rigidity and vanishing theorems for translating solitons.

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

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and arithmetic group theory, that certain hyperbolic 4-manifolds contain L-spaces as hypersurfaces.

We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.

We prove a vanishing result for critical points of the supersymmetric nonlinear sigma model on complete non-compact Riemannian manifolds of positive Ricci curvature that admit an Euclidean type Sobolev inequality, assuming that the dimension of the domain is bigger than two and that a certain energy is sufficiently sma…

We study the homotopy type of the harmonic compactification of the moduli space of a 2-cobordism S with one outgoing boundary component, or equivalently of the space of Sullivan diagrams of type S on one circle. Our results are of two types: vanishing and non-vanishing. In our vanishing results we are able to show that…

Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these cases.

Vanishing gradients hinder reinforcement finetuning of language models.

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