On the critical maps of the dirichlet functional with volume constraint

• Koh, Young-Mee (Department of Mathematics, The University of Suwon, pp. O. Box 77 & 78, Suwon)
• Published : 1995.08.01

Abstract

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$E(u) = \frac{2}{1} \int_{T} \mid\nabla u\mid^2 d\omega$$ and the volume functional by $$V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege$$.