Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 32 Issue 2
- /
- Pages.303-308
- /
- 1995
- /
- 1015-8634(pISSN)
- /
- 2234-3016(eISSN)
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}