Equilibrium Capillary Surfaces

Capillarity phenomena are all about us; anyone who has seen a drop of dew on a plant leaf or the spray from a waterfall has observed them. Apart from their frequently remarked poetic qualities, phenomena of this sort are so familiar as to escape special n

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Editors

M. Artin

S.S. Chern 1M. Frohlich E. Heinz H. Hironaka L. Hormander S. Mac Lane c.c. Moore IK Moser M. Nagata W. Schmidt D.S. Scott Ya.G. Sinai 1. Tits B.L. van der Waerden M. Waldschmidt S. Watanabe

F. Hirzebruch

Managing Editors

M. Berger B. Eckmann

S.RS. Varadhan

Grundlehren der mathematischen Wissenschaften A Series of Comprehensive Studies in Mathematics

A Selection 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244.

Dold: Lectures on Algebraic Topology Beck: Continuous Flows in the Plane Schmetterer: Introduction to Mathematical Statistics Schoeneberg: Elliptic Modular Functions Popov: Hyperstability of Control Systems Nikol'skii: Approximation of Functions of Several Variables and Imbedding Theorems Andre: Homologie des Algebres Commutatives Donoghue: Monotone Matrix Functions and Analytic Continuation Lacey: The Isometric Theory of Classical Banach Spaces Ringel: Map Color Theorem GihmaniSkorohod: The Theory of Stochastic Processes I ComfortiNegrepontis: The Theory of Ultrafilters Switzer: Algebraic Topology~Homotopy and Homology Shafarevich: Basic Alegebraic Geometry van der Waerden: Group Theory and Quantum Mechanics Schaefer: Banach Lattices and Positive Operators P6lyalSzego: Problems and Theorems in Analysis II Stenstrom: Rings of Quotients GihmaniSkorohod: The Theory of Stochastic Process II DuvantJLions: Inequalities in Mechanics and Physics Kirillov: Elements of the Theory of Representations Mumford: Algebraic Geometry I: Complex Projective Varieties Lang: Introduction to Modular Forms BerghJUifstrom: Interpolation Spaces. An Introduction Gilbarg/Trudinger: Elliptic Partial Differential Equations of Second Order SchUtte: Proof Theory Karoubi: K-Theory, An Introduction GrauertiRemmert: Theorie der Steinschen Riiume Segal/Kunze: Integrals and Operators Hasse: Number Theory Klingenberg: Lectures on Closed Geodesics Lang: Elliptic Curves: Diophantine Analysis GihmaniSkorohod: The Theory of Stochastic Processes III StroockiVaradhan: Multi-dimensional Diffusion Processes Aigner: Combinatorial Theory DynkinlYushkevich: Markov Control Processes and Their Applications GrauertiRemmert: Theory of Stein Spaces Kothe: Topological Vector-Spaces II Graham/McGehee: Essays in Commutative Harmonic Analysis Elliott: Probabilistic Number Theory I Elliott: Probabilistic Number Theory II Rudin: Function Theory in the Unit Ball of C" HuppertiBlackburn: Finite Groups I HuppertiBlackburn: Finite Groups II KubertiLang: Modular Units

cOlllinued after Index

Robert Finn

Equilibrium Capillary Surfaces With 98 lllustrations

Springer-Verlag NewYork Berlin Heidelberg Tokyo

Robert Finn Department of Mathematics Stanford University Stanford, CA 94305 U.S.A.

AMS Classifications: 53C80, 53C42

Library of Congress Cataloging-in-Publication Data Finn, Robert. Equilibrium capillary surfaces. (Grundlehren der mathematischen Wissenschaften; 284)