A double mean field equation related to a curvature prescription problem

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Double tori solution to an equation of mean curvature and Newtonian potential

Studies of near periodic patterns in many self-organizing physical and biological systems give rise to a nonlocal geometric problem in the entire space involving the mean curvature and the Newtonian potential. One looks for a set in space of the prescribed volume such that on the boundary of the set the sum of the mean curvature of the boundary and the Newtonian potential of the set, multiplied...

A Remark on Soliton Equation of Mean Curvature Flow

with II(X,Y ) = DXY −∇XY, for tangential vector fields X,Y on Σ. We define the mean curvature vector field (in short, MCV) by H = trΣII. In recent years, many people are interested in studying the evolution of the immersion F : Σ → Mn+k along its Mean Curvature Flow (in short, just say MCF). The MCF is defined as follows. Given an one-parameter family of sub-manifolds Σt = Ft(Σ) with immersions...

A nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules

In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...

Solutions to the mean curvature equation by fixed point methods

We give conditions on the boundary data, in order to obtain at least one solution for the problem (1) below, withH a smooth function. Our motivation is a better understanding of the Plateau’s problem for the prescribed mean curvature equation.