相关论文: Maximum Principles and Consequences for $\gamma$-t…
We address the classification of ancient solutions to fully nonlinear curvature flows for hypersurfaces. Under natural conditions on the speed of motion we classify ancient solutions which are convex, noncollapsing, uniformly two-convex and…
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation…
Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces…
We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $\alpha>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex…
We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…
Obstructions to the existence of spacelike solitons depending on the growth of the mean curvature $H$ are proved for Lorentzian products $(M\times \mathbb{R}, \bar g=g_M-dt^2)$ with lowerly bounded curvature. The role of these bounds for…
This paper contains a generalization of the convex ideal case of the Thurston-Andreev theorem when the genus is greater than 1. The heart of the paper concerns taking formal angle data on a surface and ``conformally flowing'' this formal…
We present a theory of voltage-induced spin-transfer torques in ballistic non-collinear spin valves. The torkance on one ferromagnetic layer is expressed in terms of scattering coefficients of the whole spin valve, in analogy to the…
In this paper, we prove an optimal inequality between the potential function of a complete Schouten soliton and the norm of its gradient. We also prove that these metrics have bounded scalar curvature of defined sign. As an application, we…
In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally…
Non-topological solitons such as Q-balls and Q-shells have been studied for scalar fields invariant under global and gauged U(1) symmetries. We generalize this framework to include a Proca mass for the gauge boson, which can arise either…
An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects related to the emission and…
We obtain localized field configurations with finite energy in a ($2+1$)-dimensional model with Maxwell and Chern-Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the $U(1)$…
In this paper, we generalize Magnanini-Sakaguchi's result [MS3] from Euclidean space to spaces of constant curvature. More precisely, we show that if a conductor satisfying the exterior geodesic sphere condition in the space of constant…
A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance…
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the…
A gauged (2+1)-dimensional version of the Skyrme model is investigated. The gauge group is $U(1)$ and the dynamics of the associated gauge potential is governed by a Maxwell term. In this model there are topologically stable soliton…
A set of integral relations for rotational and translational zero modes in the vicinity of the classical soliton solution are derived from the particle-like properties of the latter. The validity of these all relations is considered for a…
In this paper, we first discuss some connections between template theory and the description of basic sets of Smale flows on 3-manifolds due to F. B\'eguin and C. Bonatti. The main tools we use are symbolic dynamics, template moves and some…
We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2. Our main results states that tangential balls in $\mathbb R^n$ under any flat flow with a bounded…