Related papers: A characterization of the Ejiri torus in $S^{5}$

Using a new estimate for the Peng-Terng invariant and the multiple-parameter method, we verify a rigidity theorem on the stronger version of Chern Conjecture for minimal hypersurfaces in spheres. More precisely, we prove that if $M$ is a…

Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a…

The major breakthroughs in the understanding of topological materials over the past decade were all triggered by the discovery of the Z$_2$ topological insulator (TI). In three dimensions (3D), the TI is classified as either "strong" or…

Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…

In this paper, we study Riemannian functionals defined by $L^2$-norms of Ricci curvature, scalar curvature, Weyl curvature, and Riemannian curvature. We try to understand stability of their critical points that are products of Einstein…

We show that the 2-torus in ${\mathbb R}^3$ is a critical point of a sequence of functionals ${\cal F}_{n}$ ($n=1,2,3, \cdots$) defined over compact 2-surfaces in ${\mathbb R}^3$. When the Lagrange function ${\cal E}$ is a polynomial of…

Let $M$ be a Riemannian 3-manifold of nonnegative Ricci curvature, Ric $\geq 0.$ We suppose that $M$ is conformally flat and simply connected or more generally that it admits a conformal immersion into the standard 3-sphere. Let $\Sigma$ be…

On the space of isometric embeddings $f_g$ of metrics $g$ on a manifold $M^n$ into the standard $(\mb{S}^{\tn=\tn(n)},\tg)$, we consider the total exterior scalar curvature $\Theta_{f_g}(M)$, and squared $L^2$ norm of the mean curvature…

We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical initial surfaces with Willmore energy below $8\pi$ we show long…

We use the generalized Minkowski billiard characterization of the EHZ-capacity of Lagrangian products in order to reprove that the $4$-dimensional Viterbo conjecture holds for the Lagrangian products (any triangle/parallelogram in…

In this paper, we prove that a closed minimally immersed hypersurface $M^4\subset\mathbb S^5$ with constant $S:=\sum\limits_{i=1}^4\lambda_i^2$ and $A_3:=\sum\limits_{i=1}^4\lambda_i^3$ whose scalar curvature $R_M$ is nonnegative must be…

Examples of aspherical closed symplectic 4-manifolds are presented whose Sullivan minimal models are (1,n)-formal for any n, without being formal. They have as cohomology algebra, signature, canonical class, those of a product of a closed…

In analogy with the maximal tensor product of $C^*$-algebras, we define the ``maximal" tensor product $E_1\otimes_\mu E_2$ of two operator spaces $E_1$ and $E_2$ and we show that it can be identified completely isometrically with the sum of…

We consider the quintic nonlinear Schr{\"o}dinger on the circle. By applying a Birkhoff procedure and a KAM theorem, we exihibit a three dimension invariant torus that is linearly unstable. In comparison, we also prove that two dimensional…

The study of minimal surfaces has a long history, due to the important applications. Given a fixed boundary, one wants to minimise the surface area: this can be used, for example, to minimise the area of the roof of a building. Similarly,…

A Kahler-type form is a symplectic form compatible with an integrable complex structure. Let M be either a torus or a K3-surface equipped with a Kahler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in M has…

We consider a class of Hilbert-Schmidt integral operators with an isotropic, stationary kernel acting on square integrable functions defined on flat tori. For any fixed kernel which is positive and decreasing, we show that among all…

In this paper we build an explicit example of a minimal bubble on a Willmore surface, showing there cannot be compactness for Willmore immersions of Willmore energy above $16 \pi$. Additionnally we prove an inequality on the second residue…

We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which…

A closed surface evolving under mean curvature flow becomes singular in finite time. Near the singularity, the surface resembles a self-shrinker, a surface that shrinks by dilations under mean curvature flow. If the singularity is modeled…