Variations of Surfaces
Ulrich Pinkall, Oliver Gross · Compact textbooks in mathematics · 2024
Abstract We derive the basics of Vector Calculus on surfaces and explore variations of surfaces. In particular, we compute the variational derivative of the area form $$\det $$ det and of the shape operator A. We show that the critical points of the area functional are the surfaces with mean curvature $$H=0$$ H = 0 .