Multiple solutions to the Plateau problem for nonconstant mean curvature

Multiple Solutions to the Planar Plateau Problem

We give existence and nonuniqueness results for simple planar curves with prescribed geodesic curvature.

Translating Solutions to Lagrangian Mean Curvature Flow

We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an L bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee, and M.-P. Tsui, shows that these conditions are optimal.

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

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.

Weak Solutions for the Mean Curvature Flow of Planar Graphs