English
Related papers

Related papers: A remark on $\Lambda^2$-enlargeable manifolds

200 papers

We generalize the splitting theorem of Cai-Galloway for complete Riemannian manifolds with $\Ric\geq-(n-1)$ admitting a family of compact hypersurfaces tending to infinity with mean curvatures tending to $n-1$ sufficiently fast to the…

Differential Geometry · Mathematics 2013-07-04 Jeffrey S. Case , Peng Wu

In this paper, we investigate the Dirichlet problem of Laplacian on complete Riemannian manifolds. By constructing new trial functions, we obtain a sharp upper bound of the gap of the consecutive eigenvalues in the sense of the order, which…

Differential Geometry · Mathematics 2016-12-21 Lingzhong Zeng

We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some…

Quantum Physics · Physics 2023-03-24 Michael Liaofan Liu , Florian Kanitschar , Amir Arqand , Ernest Y. -Z. Tan

By way of a complete integration of the Friedmann equations, in terms of observables, it is shown that for the cosmological constant $\Lambda > 0$ there exist non-flat FLRW models for which the total density parameter $\Omega$ remains $\sim…

Astrophysics · Physics 2009-11-10 Kayll Lake

In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on $m$-dimensional closed Riemannian manifold and prove that it admits a unique local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial data is…

Analysis of PDEs · Mathematics 2018-07-04 Boling Guo , Zonglin Jia

We show that for entire maps of the form $z \mapsto \lambda \exp(z)$ such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This…

Dynamical Systems · Mathematics 2009-02-18 Neil Dobbs , Bartlomiej Skorulski

Two Riemannian manifolds are said to be isospectral if the associated Laplace-Belttrami operators have the same eigenvalue spectrum. If the manifolds have boundary, one specifies DIrichlet or Neumann isospectrality depending on the boundary…

dg-ga · Mathematics 2008-02-03 Carolyn S. Gordon , Edward N. Wilson

A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…

Optimization and Control · Mathematics 2023-09-22 Amos Uderzo

In this paper we study the behaviour of the continuous spectrum of the Laplacian on a complete Riemannian manifold of bounded curvature under perturbations of the metric. The perturbations that we consider are such that its covariant…

Spectral Theory · Mathematics 2007-05-23 Werner Mueller , Gorm Salomonsen

We introduce a direct generalization of the Weinstein conjecture to closed, Lichnerowicz exact, locally conformally symplectic manifolds, (for short $\lcs$ manifolds). This conjectures existence of certain 2-curves in the manifold, which we…

Symplectic Geometry · Mathematics 2023-10-16 Yasha Savelyev

We introduce a curvature-dimension condition for autonomous Lagrangians on weighted manifolds, which depends on the Euler-Lagrange dynamics on a single energy level. By generalizing Klartag's needle decomposition technique to the Lagrangian…

Differential Geometry · Mathematics 2026-02-11 Rotem Assouline

In this paper, we study \lambda-biharmonic Riemannian submersions, which generalize biharmonic Riemannian submersions. We prove non-existence results for \lambda-biharmonic Riemannian submersions from (n + 1)-dimensional Riemannian…

Differential Geometry · Mathematics 2026-05-18 Shun Maeta , Miho Shito

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…

Analysis of PDEs · Mathematics 2013-06-11 N. V. Krylov

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…

Differential Geometry · Mathematics 2011-05-10 Camillo De Lellis , Peter M. Topping

We prove that every Berwald manifold with non-zero flag curvature is Riemannian. This result provides an extension of Numata and Szabo's rigidity theorems. We show that every positively curved constant isotropic Berwald manifold is…

Differential Geometry · Mathematics 2026-01-29 A. Tayebi , B. Najafi

We prove that for continuous Lorentz-Finsler spaces timelike completeness implies inextendibility. Furthermore, we prove that under suitable locally Lipschitz conditions on the Finsler fundamental function the continuous causal curves that…

General Relativity and Quantum Cosmology · Physics 2019-09-30 E. Minguzzi , S. Suhr

In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized…

Differential Geometry · Mathematics 2017-03-30 Li Ma

We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this…

Differential Geometry · Mathematics 2025-08-26 Theodoros Vlachos

We consider a Laplace eigenfunction $\varphi_\lambda$ on a smooth closed Riemannian manifold, that is, satisfying $-\Delta \varphi_\lambda = \lambda \varphi_\lambda$. We introduce several observations about the geometry of its vanishing…

Analysis of PDEs · Mathematics 2017-07-18 Bogdan Georgiev , Mayukh Mukherjee

We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form $\boldsymbol{\sigma} \times \mathbb{R}$, with…

High Energy Physics - Theory · Physics 2025-08-14 Dionysios Anninos , Damián A. Galante , Chawakorn Maneerat