Related papers: Eigenvalues of harmonic almost submersions
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…
This paper is devoted to the study of the conformal spectrum (and more precisely the first eigenvalue) of the Laplace-Beltrami operator on a smooth connected compact Riemannian surface without boundary, endowed with a conformal class. We…
For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on…
A consistent approach to the description of integral coordinate invariant functionals of the metric on manifolds ${\cal M}_{\alpha}$ with conical defects (or singularities) of the topology $C_{\alpha}\times\Sigma$ is developed. According to…
In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed…
We study the extrinsic geometry of isometric immersions into Riemannian manifolds of co-dimension one via a fourth-order geometric evolution of the shape operator. Motivated by bi-harmonic map theory and generalized Chen's conjecture, we…
Our goal of this paper is to give a complete characterization of all holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains and establish a corresponding Schwarz lemma for holomorphic mappings with…
We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $\Omega$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of this problem, which depends only on the dimension, a lower…
We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.
The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…
We study generic Riemannian submersions from nearly Kaehler manifolds onto Riemannian manifolds. We investigate conditions for the integrability of various distributions arising for generic Riemannian submersions and also obtain conditions…
The classification of the possible equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in mathematical physics. In this paper it is proved that the equilibrium shapes are isoparametric…
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide…
Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa--Holm equations are well-studied examples.A beautiful approach to well-posedness is…
We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two. These foliations produce local complex-valued harmonic…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…