## Advances in Differential Equations

- Adv. Differential Equations
- Volume 15, Number 5/6 (2010), 503-530.

### Construction of complete embedded self-similar surfaces under mean curvature flow. Part II

#### Abstract

We study the Dirichlet problem associated to the equation for self-similar surfaces under mean curvature flow for graphs over the Euclidean plane with a disk removed. We show the existence of a solution provided the boundary conditions on the boundary circle are small enough and satisfy some symmetries.

#### Article information

**Source**

Adv. Differential Equations Volume 15, Number 5/6 (2010), 503-530.

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355854679

**Mathematical Reviews number (MathSciNet)**

MR2643233

**Zentralblatt MATH identifier**

1200.53061

**Subjects**

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

#### Citation

Nguyen, Xuan Hien. Construction of complete embedded self-similar surfaces under mean curvature flow. Part II. Adv. Differential Equations 15 (2010), no. 5/6, 503--530. https://projecteuclid.org/euclid.ade/1355854679.