References on Mathematical Surface

Differential Equations, Mechanics, and Computation

Differential Geometry on Surfaces

A Modern Course on Curves and Surfaces , by Richard S Palais. curves_surfaces_palais.pdf.

Lecture notes on curves and surfaces in R3 , by Chuu-Lian Terng. Surfaces_in_R3.pdf.

Minimal Surfaces

[K2] H. Karcher, Construction of minimal surfaces, in “Surveys in Geometry”, Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256, Bonn, 1989, pp. 1–96.

For a discussion of techniques for creating minimal surfaces with various qualitative features by appropriate choices of Weierstrass data, see either [KWH], or pages 192–217 of [DHKW].

[KWH] H. Karcher, F. Wei, and D. Hoffman, The genus one helicoid, and the minimal surfaces that led to its discovery, in “Global Analysis in Modern Mathematics, A Symposium in Honor of Richard Palais’ Sixtieth Birthday”, K. Uhlenbeck Editor, Publish or Perish Press, 1993.

[DHKW] U. Dierkes, S. Hildebrand, A. Kuster, and O. Wohlrab, Minimal Surfaces I, Grundlehren der math. Wiss. v. 295 Springer-Verlag, 1991.

Plane Curves

For plane curves and geometry, see: