arXiv research

In this article, we generalize the classical Bochner-Weitzenböck theorem for manifolds satisfying an integral pinching on the curvature. We obtain the vanishing of Betti numbers under integral pinching assumptions on the curvature, and characterize the equality case. In particular, we reprove and extend to higher degre…

Paper proves pinching theorem for minimal surfaces in spheres.

Ricci flow on flat manifolds converges to Euclidean space under curvature pinching.

Study pinches gradient solitons using curvature estimates.

Study pinched submanifolds, proving homology vanishing results.

In a previous paper, we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfy an integral pinching. In this article, we use the same integral Bochner technique to extend the results in dimension three. Then, by using the classification of closed thre…

Study integral bounds for submanifolds in low codimension with topological implications.

We prove that a $n$-dimensional, $4 \leq n \leq 6$, compact gradient shrinking Ricci soliton satisfying a $L^{n/2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^{n}$. The proof relies mainly on sharp algebraic curvature estimates, the Yamabe-Sobolev inequality and an improved rigidity result f…

We prove that some Riemannian manifolds with boundary under an explicit integral pinching are spherical space forms. Precisely, we show that 3-dimensional Riemannian manifolds with totally geodesic boundary, positive scalar curvature and an explicit integral pinching between the $L^2$-norm of their scalar curvature and…

Proves long-time Ricci flow existence and topological rigidity for pinched integral curvature manifolds.

In this paper we prove that, under an explicit integral pinching assumption between the $L^2$-norm of the Ricci curvature and the $L^2$-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits an Einstein metric with positive curvature. In particular this implies that the manifold is diff…

We prove that an $n$-dimensional, $n\geq4$, compact gradient shrinking Ricci soliton satisfying a $L^{\frac n2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^n$, which improves the rigidity theorem given by G. Catino (arXiv:1509.07416vl).

The paper examines ancient solutions of mean curvature flow in space forms with curvature pinching conditions.

The paper proves geometric inequalities for pinched convex hypersurfaces in de Sitter space.

In this note we characterize compact hypersurfaces of dimension $n\geq 2$ with constant mean curvature $H$ immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when $n\geq 3$ and $H\neq 0$, they are locally contained in a rotational h…

The paper examines rigidity of special submanifolds in spheres with curvature constraints.

Study focuses on classifying special geometric structures.

Sharp curvature pinching for mean curvature flow in spheres proved.

Proves a weak version of Perdomo Conjecture on minimal hypersurfaces.

We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume manifold with pinched negative sectional curvature, we show that the essential spect…

The paper establishes eigenvalue inequalities for a specific operator on curved spaces.

In this paper, by using monotonicity formulas for vector bundle-valued $p$-forms satisfying the conservation law, we first obtain general $L^2$ global rigidity theorems for locally conformally flat (LCF) manifolds with constant scalar curvature, under curvature pinching conditions. Secondly, we prove vanishing results …

Study pinching constants for Kähler manifolds with positive curvature.

Study on 4D solitons with curvature constraints.

Three-manifolds with non-negative pinched Ricci curvature have complete Ricci flows.

Study a volume preserving flow using symmetric polynomials without curvature pinching assumptions.

Study pinched self-dual Weyl curvature in compact 4-manifolds.

We refine a metric bunching estimate for pinched manifolds.

Paper proves Hamilton's pinching theorem using mean curvature flow.

The paper improves inequalities for Kähler-Einstein manifolds using curvature conditions.

Flat Yang-Mills connections on pinched manifolds.

The paper pinches curvature in expanding Ricci solitons.

This paper extends 3D results to higher dimensions, proving compactness for PIC1 pinched manifolds.

In this article, we consider the Angenent-Caputo-Knopf's Ricci Flow through neckpinch singularities. We will explain how one can see the A-C-K's Ricci flow through a neckpinch singularity as a flow of integral current spaces. We then prove the continuity of this weak flow with respect to the Sormani-Wenger Intrinsic Fl…

Compact shrinkers with curvature pinching conditions proven.

Alternative proof of flatness for Ricci-pinched 3-manifolds.

We classify compact conformally flat $n$-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either $\mathbb{S}^{n}$ with the round metric, $\mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with the product metric or $\mathbb{S}^{1…

Proves CLT for Brownian paths on pinched negative curvature manifolds.

The study pinches the rigidity of self-shrinking surfaces in mean curvature flow.

Study pinched submanifolds in space forms, proving rigidity results.

Study shows pinched solutions of mean curvature flow blow up in codimension one.

We consider a totally nonsymplectic Anosov action of Z^k which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is C^\infty--conjugate to an action by affine automorphisms. We also obtain similar global rigidity results for actions on an arbitrar…

Study neck pinches in Lagrangian flows, proving stability and introducing new singularities.

Study on G2-structures on solvmanifolds, focusing on Laplacian solitons and Ricci pinching.

Ancient solutions to high codimension flow pinched by spheres.

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.

Study on surfaces pinched by curvature in space forms converging under specific conditions.

The study finds optimal curvature pinching in Heintze groups.