Variational Problems in Differential Geometry

Bielawski, RogerRoger Bielawski is Professor of Geometry at the University of Leeds and specializes in gauge theory and hyperkähler geometry.Houston, KevinKevin Houston is a senior lecturer at the University of Leeds and specializes in singularity theory. He is the author of over twenty published research papers and author of the undergraduate textbook How to Think Like a Mathematician published by Cambridge University Press in 2009.Speight, MartinMartin Speight is Reader in Mathematical Physics at the University of Leeds. He specializes in the applications of differential geometry to theoretical physics, particularly the study of topological solitons.

The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kähler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduate students and postdoctoral researchers. With a mix of expository and original papers this volume is an excellent reference for experienced researchers in geometric variational problems, as well as an ideal introduction for graduate students. It presents all the varied methods and techniques used in attacking geometric variational problems and includes many up-to-date results.

The state of the art from an internationally respected line up of authors working in geometric variational problems.

1. Preface; 2. The supremum of first eigenvalues of conformally covariant operators in a conformal class Bernd Ammann and Pierre Jammes; 3. K-Destabilizing test configurations with smooth central fiber Claudio Arezzo, Alberto Della Vedova and Gabriele La Nave; 4. Explicit constructions of Ricci solitons Paul Baird; 5. Open iwasawa cells and applications to surface theory Josef F. Dorfmeister; 6. Multiplier ideal sheaves and geometric problems Akito Futaki and Yuji Sano; 7. Multisymplectic formalism and the covariant phase space Frédéric Hélein; 8. Nonnegative curvature on disk bundles Lorenz J. Schwachhöfer; 9. Morse theory and stable pairs Richard A. Wentworth and Graeme Wilkin; 10. Manifolds with k-positive Ricci curvature Jon Wolfson.