Papers Available Online*


Flat Curves (with Joel Langer), Mediterranean Journal of Mathematics, (2017) to appear.

The Trefoil, (with Joel Langer), Milan Journal, 82 (2014),161-182.

Numerical Approximation of the Field of Values of the Inverse of a Large Matrix (with Michiel Hochstenback and Paul Zachlin), Textos de Matematica 44 (2013),59-71.

Subdividing the Trefoil by Origami (with Joel Langer), Geometry 1 (2012).

The Lemniscatic Chessboard, (with Joel Langer), Forum Geometricorum 11 (2011), 183{199.

Reflections on the lemniscate of Bernoulli: The forty-eight faces of a mathematical gem, (with Joel Langer), Milan. J. Math., 78, Number 2 (2010), 643--682.

When is a Curve an Octahedron?, (with Joel Langer), American Mathematical Monthly, 117, Number 10, December 2010 , pp. 889-902.

Lectures on Elastic Curves and Rods, Curvature and Variational Modeling in Physics and Biophysics, Conference Proceedings of the American Institute of Physics, 1002 (2008), 3-32.

Foci and Foliations of Algebraic Curves, (with Joel Langer), Milan. Journal of Mathematics 75 (2007), 225--271.

Eigenvalue inclusion regions from inverses of shifted matrices, (with Michiel E. Hochstenbach and Paul F. Zachlin), Linear Algebra and its Applications 429 (2008), 2481-2496.

The location of critical points of Finite blaschke products, Conform. Geom. Dyn. 10 (2006), 117-124.

Anti-Tamper Databases: Querying Encrypted Databases, 17th Annual IFIP WG 11.3 Working Conference on Database and Applications Security, Estes Park, Colorado, August 4-6, 2003 (with G. Ozsoyoglu and Sun S. Chung).

A New Flow on Starlike Curves in , Proc. Amer. Math. Soc. 130 (2002), 2725-2735 (with Rongpei Huang).

Diffeomorphisms of the circle and hyperbolic curvature, Conform. Geom. Dyn. 5 (2001), 1-5.

Curves whose Curvature Depends on Distance from the Origin, Am. Math. Monthly 106 (1999), 835-841.

Knot Types, Homotopies and Stability of Closed Elastic Rods, Proceedings of the London Mathematical Society (1999), 79:429-450 (with Tom Ivey).

Elasticae with Constant Slant in the Complex Projective Plane and New Examples of Willmore Tori in Five-spheres, (with M. Barros and O. Garay), Tokohu Math Journal 51 (1999), 177-192.

Lagrangian Aspects of the Kirchhoff Elastic Rod, SIAM Review 38 (1996), 605-618 (with Joel Langer). (JSTOR link)

Liouville Integrability of Geometric Variational Problems, Comment. Math. Helvetici 69 (1994), 272-280 (with Joel Langer).

Isometries of the Plane, Am. Math. Monthly 102 (1994), 628-631.

Normal Forms for Lorentzian Spaces, Nova Journal of Algebra and Geometry 3 (1994), 1-10 (with Dan Steinberg). Preprint version here.

A new structural framework for parity equation-based failure detection and isolation, Automatica Volume 26, Issue 2 , March 1990, Pages 381-388 (with Janos Gertler).

Curve-straightening in Riemannian manifolds, (with J. Langer), Ann. Global Anal. Geom. 5 (1987), 133-150.

Curve straightening and a minimax argument for closed elastic curves. Topology 24 (1985), no. 1, 75--88 (with Joel Langer).

Knotted elastic curves in R^3, (with J. Langer), J. London Math. Soc.(2) 30 (1984), 512-520.

Curves in the hyperbolic plane and mean curvature of tori in 3-space, (with J. Langer), Bull. London Math. Soc.16 (1984), 531-534.

The total squared curvature of closed curves, (with J. Langer), J. Diff. Geometry 20 (1984), 1-22.

Diffeomorphisms of the Circle and Geodesic Fields on Riemannian Surfaces of Genus One, Invent. math. 69 (1982), 229-242 (with Joel Langer).

Scattering of geodesic fields. II. Ann. of Math. (2) 110 (1979), no. 2, 205--225. (see also I)(with Herman Gluck)

Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math. 35 (1978), no. 2, 260--267.

The existence of nontriangulable cut loci, (with H. Gluck), Bull. Am. Math. Soc. 82 (1976), 599-602.

Deformation of geodesic fields, (with H. Gluck), Bull. Am. Math. Soc. 82 (1976), 571-574.

The converse to the Gauss-Bonnet theorem in PL, (with H. Gluck and K. Krigelman), J. Diff. Geometry 9 (1974), 601-616.

Preassigning curvature on polyhedra homeomorphic to the 2-sphere, J. Diff. Geometry {\bf 9} (1974), 633-638.

Here is an ancient paper of mine, never before published, on Rectilinear Crossing Numbers.

* In some cases, access is restricted.

David Singer
Professor of Mathematics
College of Arts and Sciences
Case Western Reserve University
Cleveland, Ohio 44106-7058

Phone: (216)368-2892

Fax: (216)368-5163

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