Related papers: Isotropic curve flows on $R^{n+1, n}$

Let $T$ be a $C^{1}$ competitive map on a rectangular region $R\subset \mathbb{R}^{2}$. The main results of this paper give conditions which guarantee the existence of an invariant curve $C$, which is the graph of a continuous increasing…

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of…

Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be…

We propose a geometric perspective to describe the motion of self-propelled particles moving at constant speed in d dimensions. We exploit the fact that the vector that conveys the direction of motion of the particle performs a random walk…

For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a…

In this paper, we are concerned with interactions between isoparametric theory and differential topology. Two foliations are called equivalent if there exists a diffeomorphism between the foliated manifolds mapping leaves to leaves. Using…

We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evolution is governed by a degenerate quasilinear parabolic…

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…

In [5], together with J. C. Wood, the authors gave a completely explicit formula for all harmonic maps from $2$-spheres to the unitary group $U(n)$ in terms of freely chosen meromorphic functions on $S^2$. The simplest harmonic maps are the…

Let $x\in\mathbb{R}^{n}$. For $\phi:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ and $t\in\mathbb{R}$, we put $\phi^{t}=t^{-1}\phi(xt)$. A projective flow is a solution to the projective translation equation $\phi^{t+s}=\phi^{t}\circ\phi^{s}$,…

Families of oriented lines in $\mathbb{R}^{n+1}$ are studied via their identification with submanifolds of $T\mathbb{S}^n$. In particular, families of oriented lines which are orthogonal to submanifolds in $\mathbb{R}^{n+1}$ are shown to…

We initiate a non-perturbative study of anisotropic, non-conformal and confining gauge theories that are holographically realized in gravity by generic Einstein-Axion-Dilaton systems. In the vacuum our solutions describe RG flows from a…

I study the formation of Comptonization spectra in spherically symmetric, fast moving media in a flat spacetime. I analyze the mathematical character of the moments of the transfer equation in the system-frame and describe a numerical…

In this communication, the closure formulas of von K\'arm\'an--Howarth and Corrsin equations are obtained through the Liouville theorem and the hypothesis of homogeneous isotropic incompressible turbulence. Such closures, based on the…

We study the topology of the space of all smooth asymptotically stable vector fields on $\mathbb{R}^n$, as well as the space of all proper smooth Lyapunov functions for such vector fields. We prove that both spaces are path-connected and…

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer.…

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…

Let $M$ be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on $M$ to a small tubular neighborhood of each connected component of its singular stratum is foliated-diffeomorphic to an…

In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…

We define and study the harmonic curves on domains in $\mathbb{R}^n$ into the first Heisenberg group $\mathbb{H}^1$. These are the $C^2$-regular mappings which are critical points of the second Dirichlet energy and satisfy the weak…