Variational Methods for Free Surface Interfaces : Proceedings of a Conference Held at Vallombrosa Center, Menlo Park, California, September 7–12, 1985

Vallombrosa Center was host during the week September 7-12, 1985 to about 40 mathematicians, physical scientists, and engineers, who share a common interest in free surface phenomena. This volume includes a selection of contributions by participants and also a few papers by interested scientists who were unable to attend in person. Although a proceedings volume cannot recapture entirely the stimulus of personal interaction that ultimately is the best justification for such a gathering, we do offer what we hope is a representative sampling of the contributions, indicating something of the varied and interrelated ways with which these classical but largely unsettled questions are currently being attacked. For the participants, and also for other specialists, the 23 papers that follow should help to establish and to maintain the new ideas and insights that were presented, as active working tools. Much of the material will certainly be of interest also for a broader audience, as it impinges and overlaps with varying directions of scientific development. On behalf of the organizing committee, we thank the speakers for excellent, well-prepared lectures. Additionally, the many lively informal discussions did much to contribute to the success of the conference. Front Matter....Pages i-x Optimal Crystal Shapes....Pages 1-11 Immersed Tori of Constant Mean Curvature in R 3 ....Pages 13-26 The Construction of Families of Embedded Minimal Surfaces....Pages 27-36 Boundary Behavior of Nonparametric Minimal Surfaces—Some Theorems and Conjectures....Pages 37-41 On Two Isoperimetric Problems with Free Boundary Conditions....Pages 43-51 Free Boundary Problems for Surfaces of Constant Mean Curvature....Pages 53-63 On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian Manifolds....Pages 65-75 Free Boundaries in Geometric Measure Theory and Applications....Pages 77-83 A Mathematical Description of Equilibrium Surfaces....Pages 85-89 Interfaces of Prescribed Mean Curvature....Pages 91-97 On the Uniqueness of Capillary Surfaces....Pages 99-108 The Behavior of a Capillary Surface for Small Bond Number....Pages 109-113 Convexity Properties of Solutions to Elliptic P.D.E.’S....Pages 115-121 Boundary Behavior of Capillary Surfaces Via the Maximum Principle....Pages 123-126 Convex Functions Methods in the Dirichlet Problem for Euler—Lagrange Equations....Pages 127-137 Stability of a Drop Trapped Between Two Parallel Planes: Preliminary Report....Pages 139-144 The Limit of Stability of Axisymmetric Rotating Drops....Pages 145-153 Numerical Methods for Propagating Fronts....Pages 155-164 A Dynamic Free Surface Deformation Driven by Anisotropic Interfacial Forces....Pages 165-172 Stationary Flows in Viscous Fluid Bodies....Pages 173-178 Large Time Behavior for the Solution of the Non-Steady Dam Problem....Pages 179-190 New Results Concerning the Singular Solutions of the Capillarity Equation....Pages 191-196 Continuous and Discontinuous Disappearance of Capillary Surfaces....Pages 197-204