- V. Bangert. "On the Existence of Closed Geodesics on Two-Spheres." Internat. J. Math. 4:1 (1993), 1–10.
- Richard Brent. Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice Hall, Inc., 1973.
- Manfredo P. do Carmo. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice Hall, Inc., 1976.
- J. Franks. "Geodesics on S 2 and Periodic Points of Annulus Homeomorphisms." Invent. Math. 108:2 (1992), 403–418.
- M. E. Gage. "Deforming Curves on Convex Surfaces to Simple Closed Geodesics." Indiana Univ. Math. J. 39 (1990), 1037–1059.
- M. A. Grayson. "Shortening Embedded Curves." Ann. of Math. 129 (1989), 71–111.
- J. Langer and D. A. Singer. "The Total Squared Curvature of Closed Curves." J. Diff. Geom. 20 (1984), 1–22.
- J. Langer and D. A. Singer. "Curve- Straightening in Riemannian Manifolds." Ann. Global Anal. Geom. 5 (1987), 133–150.
- A. Linnér. "Curve-Straightening in Closed Euclidean Submanifolds." Commun. Math. Phys. 138 (1991), 33–49.
- A. Linnér. "Curve-Straightening and the Palais-Smale Condition." Trans. Amer. Math. Soc. 350 9 (1998), 3743–3765.
- A. Linnér. "Symmetrized Curve-Straightening." Diff. Geo. Appl. 18 (2003), 119–146.
- A. Linnér. "Periodic Geodesics Generator." Experimental Mathematics 13:2 (2004), 199–213.
- J. W. Neuberger. Sobolev Gradients and Differential Equations. Lecture Notes in Mathematics, 1670. New York: Springer, 1997.
- E. Polak. Computational Methods in Optimization. New York: Academic Press, 1971.
- R. Renka. "Algorithm 828. DNSPLIN1: Discrete Nonlinear Spline Interpolation." ACM Trans. Math. Softw. 29:4 (2003), 1–11.
- R. Renka. "Constructing Fair Curves and Surfaces with a Sobolev Gradient Method." CAGD 21 (2004), 137–149.
- R. Renka. "Algorithm 834. glsurf — An Interactive Surface Plotting Program using OpenGL." ACM Trans. Math. Softw. 30:2 (2004), 212–217.
Discrete Periodic Geodesics in a Surface
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