Bøger af Anthony Tromba

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 book shows how to calculate arbitrarily high orders of derivatives of the Douglas Energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations.

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.

First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years.