Bücher von Stefan Hildebrandt

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "e;Solution of PDE's and Calculus of Variations"e;. The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

Why does nature prefer some shapes and not others? The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems-such as those of geometric optics-of parts of the theory.

This is the third of a three-volume treatise on minimal surfaces. It deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems.

This is the second of a three-volume treatise on minimal surfaces. It deals with basic regularity results for minimal surfaces concerning their boundary behavior at Plateau boundaries and free boundaries.

This is the first of a three-volume treatise on minimal surfaces. It covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.