Related papers: An alternative approach to Shnirelman's inequality

Let $f$ and $g$ be two volume-preserving diffeomorphisms on the cube $Q=[0,1]^{\nu}$, $\nu \geq 3$. We show that there is a divergence-free vector field $v \in L^1((0,1);L^p(Q))$ such that $v$ connects $f$ and $g$ through the corresponding…

We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is…

Let $n \in \mathbb N$, let $\zeta_{n,1},...,\zeta_{n,n}$ be a sequence of independent random variables with $\mathbb E \zeta_{n,i}=0$ and $\mathbb E |\zeta_{n,i}|<\infty$ for each $i$, and let $\mu$ be an $\alpha$-stable distribution having…

A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…

Given two continuity equations with density-dependent velocities, we provide a new formula for the Wasserstein distance between the solutions in terms of the difference of velocities evaluated at the same density. The formula is…

The $l_2$ flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the…

This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…

We construct a new finite difference method for the flow of ideal viscous isentropic gas in one spatial dimension. For the continuity equation, the method is a standard upwind discretization. For the momentum equation, the method is an…

Given an ample line bundle $L$ on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich…

We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We…

In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations as a differential…

In the conformal class of the standard metric on the $3$-sphere, we prove a quantitative refinement of the Andrews-De Lellis-Topping inequality in terms of a two-term distance to the set of minimizing conformal factors. This inequality is…

We show that for any $\epsilon<1$ and any $\mathcal{T}$ `drifting away from walls', Dirichlet's Theorem cannot be $\epsilon$-improved along $\mathcal{T}$ for Lebesgue almost every system of linear forms $Y$ (see the paper for definitions).…

This paper is devoted to establishing the convergence rate of the hypersonic similarity for the inviscid steady irrotational Euler flow over a two-dimensional Lipschitz slender wedge in $BV\cap L^1$ space. The rate we established is the…

A theorem of W. Derrick ensures that the volume of any Riemannian cube $([0,1]^n,g)$ is bounded below by the product of the distances between opposite codimension-1 faces. In this paper, we establish a discrete analog of Derrick's…

In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method…

Let $(M,g)$ be a compact $n$-dimensional Riemannian manifold with nonempty boundary and $n\geq 2$. Assume that ${\mathrm{Ric}(M)\ge (n-1)K}$ for some ${K>0}$ and that $\partial M$ has nonnegative mean curvature with respect to the outward…

We provide a bound on a natural distance between finitely and infinitely supported elements of the unit sphere of $\ell^2(\mathbb{N}^*)$, the space of real valued sequences with finite $\ell^2$ norm. We use this bound to estimate the…

We contribute to an original problem studied by Hamilton and others, in order to understand the behaviour of maximal solutions of the Ricci flow both in compact and non-compact complete orientable Riemannian manifolds of finite volume. The…

In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges…