1.6. Exercises 25 − π 4 0 π 4 − π 4 0 π 4 -4 0 4 Figure 1.13. Scherk’s first minimal surface 1.6.10. Scherk’s minimal surface. Take the minimal surface equa- tion, equation (1.47), and look for a solution of the form f(x, y) = g(x) + h(y) . (1.70) Show that the resulting differential equation is separable. Solve for g(x) and h(y) to obtain Scherk’s (first) minimal surface, f(x, y) = c ln cos (x/c) cos (y/c) . (1.71) This surface was the first minimal surface discovered after the catenoid and the helicoid. A piece of this surface, for c = 1, −π/2 x π/2, and −π/2 y π/2, is shown in Figure 1.13.
Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2014 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.