Kategoria BISAC: Mathematics >> Geometry - Analytic

Collagen: Structure and Mechanics provides a cohesive introduction to this biological macromolecule and its many applications in biomaterials and tissue engineering.

Graduate students and postdoctoral researchers in the fields of materials, (bio-)engineering, physics, chemistry and biology will gain an understanding of the structure and mechanical behavior of type I collagen and collagen-based tissues in vertebrates, across all length scales from the molecular (nano) to the organ (macro) level. Written in a clear and didactic manner, this volume includes current knowledge on the...

Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and...

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in other areas of mathematics and in the applied fields.

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincare metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.

The existence and uniqueness of the ambient metric at the formal power series level is treated in...

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation,...