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Monday, February 15, 2016

Differential Geometry and Its Application - Exercise 3.1.10

Problem:


Solution:

A surface is minimal if its mean curvature is 0, so the sum of the eigenvalues is 0. Let the eigenvalues be $ x $ and $ y $ respectively, the Gaussian curvature K is then the product $ xy = x(-x) = -x^2 \le 0 $

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