Related papers: Interior estimates for Translating solitons of the…

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral operators.…

We fix a maximal order $\mathcal O$ in $\F=\R,\C$ or $\mathbb{H}$, and an $\F$-hermitian form $Q$ of signature $(n,1)$ with coefficients in $\mathcal O$. Let $k\in\N$. By applying a lattice point theorem on the $\F$-hyperbolic space, we…

We determine the asymptotic density $\delta_k$ of the set of ordered $k$-tuples $(n_1,...,n_k)\in \N^k, k\ge 2$, such that there exists no prime power $p^a$, $a\ge 1$, appearing in the canonical factorization of each $n_i$, $1\le i\le k$,…

We consider translators to the extrinsic flows in $\mathbb R^n\times\mathbb R$ and $\mathbb H^n\times\mathbb R$ (called $r$-mean curvature flows or $r$-MCF, for short) whose velocity functions are the higher order mean curvatures $H_r.$ We…

This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear…

The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is proven by functional integrations. As a…

In this work we show that $2$-dimensional, simply connected, translating solitons of the mean curvature flow embedded in a slab of $\mathbb{R}^3$ with entropy strictly less than $3$ must be mean convex and thus, thanks to a result by J.…

Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of…

Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane.…

We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in Khinchin' result, then we deduce a sharp…

It is shown that the lowest (second) order truncation of the Carleman linearization of the fluid equations (C2) recovers not only the initial transient of the time evolution but also its late stage, namely the steady-state solution. This…

In this study, we deal with non-degenerate translators of the mean curvature flow in the well-known hyperbolic Einstein's static universe. We classify translators foliated by horospheres and rotationally invariant ones, both space-like and…

In the present work, we revisit the topic of translational eigenmodes in discrete models. We focus on the prototypical example of the discrete nonlinear Schr{\"o}dinger equation, although the methodology presented is quite general. We…

A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a $K^\alpha$-translator of the flow by the powers of Gauss curvature if satisfies $K^\alpha= \langle N,\vec{v}\rangle$, $\alpha \neq 0$, where $K$ is the Gauss curvature, $N$…

We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain $\Omega…

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer…

We study ancient mean curvature flows in $\mathbb{R}^{n+1}$ whose tangent flow at $-\infty$ is a shrinking cylinder $\mathbb{R}^{k}\times S^{n-k}(\sqrt{2(n-k)|t|})$, where $1\leq k\leq n-1$. We prove that the cylindrical profile function…

Q-balls are non-topological solitons in a large family of field theories. We focus on the existence of $U(1)$ gauged Q-balls for a field theory with sixth-order potential. The problem can be reduced to proving the existence of critical…

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the…