Christine Guenther

Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.

This textbook is a comprehensive overview of the development of cell-based biopharmaceuticals. Beginning with the underlying biology of stem cell and cell-based products, it traces the long and complex journey from preclinical concept to initiation of a pivotal clinical trial and the potential business model behind it.The book also takes into consideration the different regulatory landscapes and their continuous evolution in Europe, North America and other parts of the world. The authors describe a path to manufacture a clinical grade therapeutic that passes all necessary quality measures as a robust and marketable product including an outlook on next generation products and innovative strategies.This reference book is a must-have guide for any professional already active in biopharmaceuticals and anyone interested in getting involved in a scientific, medical or business capacity.