Optimal Crystal Shapes.- Immersed Tori of Constant Mean Curvature in R3.- The Construction of Families of Embedded Minimal Surfaces.- Boundary Behavior of Nonparametric Minimal Surfaces-Some Theorems and Conjectures.- On Two Isoperimetric Problems with Free Boundary Conditions.- Free Boundary Problems for Surfaces of Constant Mean Curvature.- On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian Manifolds.- Free Boundaries in Geometric Measure Theory and Applications.- A Mathematical Description of Equilibrium Surfaces.- Interfaces of Prescribed Mean Curvature.- On the Uniqueness of Capillary Surfaces.- The Behavior of a Capillary Surface for Small Bond Number.- Convexity Properties of Solutions to Elliptic P.D.E.'S.- Boundary Behavior of Capillary Surfaces Via the Maximum Principle.- Convex Functions Methods in the Dirichlet Problem for Euler-Lagrange Equations.- Stability of a Drop Trapped Between Two Parallel Planes: Preliminary Report.- The Limit of Stability of Axisymmetric Rotating Drops.- Numerical Methods for Propagating Fronts.- A Dynamic Free Surface Deformation Driven by Anisotropic Interfacial Forces.- Stationary Flows in Viscous Fluid Bodies.- Large Time Behavior for the Solution of the Non-Steady Dam Problem.- New Results Concerning the Singular Solutions of the Capillarity Equation.- Continuous and Discontinuous Disappearance of Capillary Surfaces.
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.
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