Related papers: Rigidity of Euler Products
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
Simple Hamiltonian systems, such as mathematical pendulum or Euler equations for rigid body, are solved without computation. It is nothing but a joke but maybe you will find it nice.
We study the distribution of products of conjugacy classes in finite simple groups, obtaining various effective uniformity results, which give rise to an approximation to a conjecture of Thompson. Our results, combined with work of Gowers…
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the…
We prove the existence of periodic orbits for steady $C^\omega$ Euler flows on all Riemannian solid tori. By using the correspondence theorem from part I of this series, we reduce the problem to the Weinstein Conjecture for solid tori. We…
We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian…
By using certain idea developed in minimal submanifold theory we study rigidity problem for self-shrinkers in the present paper. We prove rigidity results for squared norm of the second fundamental form of self-shrinkers, either under…
This note is devoted to a rigorous derivation of rigid-plasticity as the limit of elasto-plasticity when the elasticity tends to infinity.
We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $\mu_{min}(L \otimes M) = \mu_{min}(L)\mu_{min}(M)$ for all Euclidean lattices $L$ and $M$. We prove that this is the…
The Rayleigh equation, which is the linearized Euler equations near a shear flow in vorticity formulation, is a key ingredient in the study of the long time behavior of solutions of linearized Euler equations, in the study of the linear…
In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…
We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by…
We prove that the notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no ``continuity constants'' are required. The proof is by…
We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations…
The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…
In this paper we introduce techniques to gauge the torsion of the tensor product $A\otimes_RB$ of two finitely generated modules over a Noetherian ring $R$. The outlook is very different from the study of the rigidity of Tor carried out in…