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- Dennis DeTurck
- 2003

In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S. In fact, he shows that the original metric can be deformed into the constant-curvature metric by… (More)

- Jason Cantarella, Dennis DeTurck, Herman Gluck
- The American Mathematical Monthly
- 2002

Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator… (More)

The writhing number of a curve in Euclidean 3-space, introduced by Călugăreanu (1959-61) and named by Fuller (1971), is the standard measure of the extent to which the curve wraps and coils around itself; it has proved its importance for molecular biologists in the study of knotted duplex DNA and of the enzymes which affect it. The helicity of a vector… (More)

- Dennis DeTurck, Herman Gluck, +4 authors DAVID SHEA VELA-VICK
- 2013

To each three-component link in Euclidean 3–space, we associate a generalized Gauss map from the 3–torus to the 2–sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. This generalized Gauss… (More)

- John R. Senior, Ming F. Johnson, Dennis DeTurck, Franco Bazzoli, Enrico Roda
- Gastroenterology
- 1990

The rate of decrease of gallstone diameter appeared to be linear with oral bile acid treatment time, as estimated by inspection of graphic data of individual patient serial oral cholecystograms. A theoretical basis for this model was derived. The hypothesis of diameter decrease proportional to treatment time was tested with data from 223 patients with… (More)

To Julius Shaneson on the occasion of his 60th birthday

- Jason Cantarella, Dennis DeTurck, Herman Gluck, Mikhail Teytel
- 1998

The helicity of a smooth vector field defined on a domain in 3-space is the standard measure of the extent to which the field lines wrap and coil around one another; it plays important roles in fluid mechanics, magnetohydrodynamics and plasma physics. In this report we show how the relation between energy and helicity of a vector field is influenced by the… (More)

For (M, g) a compact Riemannian manifold, we consider the spectra of the Laplace-Beltrami operator and of the Schrödinger operator "Laplacian plus potential" acting on L (M, g). Two Riemannian manifolds are said to be isospectral if their associated Laplacians have the same spectra, and two potentials on the same Riemannian manifold are said to be… (More)