Geometric Methods in Elastic Theory of Membranes in Liquid Crystal Phases

This is the second edition of the book Geometric Methods in Elastic Theory of Membranes in Liquid Crystal Phases published by World Scientific in 1999. This book gives a comprehensive treatment of the conditions of mechanical equilibrium and the deformation of membranes as a surface problem in differential geometry. It is aimed at readers engaging in the field of investigation of the shape formation of membranes in liquid crystalline state with differential geometry. The material chosen in this book is mainly limited to analytical results. The main changes in this second edition are: we add a chapter (Chapter 4) to explain how to calculate variational problems on a surface with a free edge by using a new mathematical tool — moving frame method and exterior differential forms — and how to derive the shape equation and boundary conditions for open lipid membranes through this new method. In addition, we include the recent concise work on chiral lipid membranes as a section in Chapter 5, and in Chapter 6 we mention some topics that we have not fully investigated but are also important to geometric theory of membrane elasticity.
Contents: Introduction to Liquid Crystal BiomembranesCurvature Elasticity of Fluid MembranesShape Equation of Lipid Vesicles and Its SolutionsGoverning Equations for Open Lipid Membranes and Their SolutionsTheory of Tilted Chiral Lipid BilayersSome Untouched TopicsAppendices
Readership: Researchers working with biomembranes.
Keywords:Geometry;Elasticity;MembraneReview:Key Features:Two kinds of mathematical technique were introduced to deal with the variational problems on a surfaceAlmost all analytic solutions to shape equations were presentedNew developments were added relative to the first edition