By Rafael López
The research of surfaces with consistent suggest curvature (CMC) is without doubt one of the major issues in classical differential geometry. in addition, CMC surfaces are very important mathematical versions for the physics of interfaces within the absence of gravity, the place they separate varied media or for capillary phenomena. additional, as such a lot suggestions utilized in the speculation of CMC surfaces not just contain geometric equipment but additionally PDE and intricate research, the speculation is usually of significant curiosity for plenty of different mathematical fields.
While minimum surfaces and CMC surfaces usually have already been taken care of within the literature, the current paintings is the 1st to offer a entire research of “compact surfaces with boundaries,” narrowing its concentration to a geometrical view. uncomplicated concerns comprise the dialogue no matter if the symmetries of the curve inherit to the outside; the potential values of the suggest curvature, sector and quantity; balance; the round boundary case and the lifestyles of the Plateau challenge within the non-parametric case. The exposition offers an outlook on contemporary study but in addition a suite of suggestions that permits the consequences to be improved to different ambient areas. during the textual content, a variety of illustrations make clear the consequences and their proofs.
The ebook is meant for graduate scholars and researchers within the box of differential geometry and particularly thought of surfaces, together with geometric research and geometric PDEs. It courses readers as much as the cutting-edge of the idea and introduces them to attention-grabbing open problems.
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Constant Mean Curvature Surfaces with Boundary (Springer Monographs in Mathematics) by Rafael López