Related papers: Persistence barcodes and Laplace eigenfunctions on…

Several uniqueness results on compact maximal hypersurfaces in a wide class of sta- bly causal spacetimes are given. They are obtained from the study of a distinguished function on the maximal hypersurface, under suitable natural first…

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in…

The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…

Motivated by applications in fluid dynamics involving the harmonic Bergman projection we aim at extending the theory of single and double layer potentials (well documented for functions with $H^1_{\ell oc}$ regularity) to locally square…

We study the covariant derivatives of an eigenfunction for the Laplace-Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant…

We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…

In this paper, classical isometric helicoidal and rotational surfaces are studied, and generalized by Bour's theorem in three dimensional Euclidean space. Moreover, the third Laplace-Beltrami operators of two classical surfaces are…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

- In this article, we prove some universal bounds on the speed of concentration on small (frequency-dependent) neighborhoods of submanifolds of L 2-norms of quasi modes for Laplace operators on compact manifolds. We deduce new results on…

We consider linear combinations of eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold $(M,g)$ and investigate a density property of their zero sets. More precisely, let $f=\sum_{k=1}^m a_k…

In this paper we develop the compactness theorem for $\lambda$-surface in $\mathbb R^3$ with uniform $\lambda$, genus, and area growth. This theorem can be viewed as a generalization of Colding-Minicozzi's compactness theorem for…

Given a compact Riemannian manifold with boundary, we prove that the limit of a sequence of embedded, almost properly embedded free boundary minimal hypersurfaces, with uniform area and Morse index upper bound, always inherits a non-trivial…

We investigate some conditions under which the Lebesgue constants or Lebesgue functions are bounded for the classical Lagrange polynomial interpolation on a compact subset of $\mathbb R$. In particular, relationships of such boundedness…

We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to…

We give uniform upper and lower bounds for the L^2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results…

We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the…

We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on…

Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…

An upper bound on the first S^1 invariant eigenvalue of the Laplacian for invariant metrics on the 2-sphere is used to find obstructions to the existence of isometric embeddings of such metrics in (R^3,can). As a corollary we prove: If the…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…