The examine of surfaces with consistent suggest curvature (CMC) is among the major themes 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 diverse media or for capillary phenomena. extra, as such a lot ideas utilized in the speculation of CMC surfaces not just contain geometric tools but additionally PDE and intricate research, the idea can also be of serious 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 provide a finished examine of “compact surfaces with boundaries,” narrowing its concentration to a geometrical view. easy concerns contain the dialogue even if the symmetries of the curve inherit to the skin; the potential values of the suggest curvature, quarter and quantity; balance; the round boundary case and the lifestyles of the Plateau challenge within the non-parametric case. The exposition presents an outlook on fresh study but in addition a suite of thoughts that enables the implications to be accelerated to different ambient areas. during the textual content, a variety of illustrations make clear the implications and their proofs.
The publication is meant for graduate scholars and researchers within the box of differential geometry and particularly concept of surfaces, together with geometric research and geometric PDEs. It publications readers as much as the cutting-edge of the idea and introduces them to fascinating open problems.
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