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13 papers · 1 filter
Complex Valued Analytic Torsion for Flat Bundles and for Holomorphic Bundles with (1,1) Connections
Sylvain E. Cappell, Edward Y. Miller
The work of Ray and Singer which introduced analytic torsion, a kind of determinant of the Laplacian operator in topological and holomorphic settings, is naturally generalized in b…
On Normalized Ricci Flow and Smooth Structures on Four-Manifolds with
Masashi Ishida, Rares Rasdeaconu, Ioana Suvaina
We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with . By using this obstruction, we study the relationship…
Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds
Maria Calle, Darren Lee
We show that there exists a metric with positive scalar curvature on S2xS1 and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborho…
Width and finite extinction time of Ricci flow
Tobias H. Colding, William P. Minicozzi
This is an expository article with complete proofs intended for a general non-specialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call t…
Width and mean curvature flow
Tobias H. Colding, William P. Minicozzi
Given a Riemannian metric on a homotopy -sphere, sweep it out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight…
A short proof of Gromov's filling inequality
Stefan Wenger
We give a very short and rather elementary proof of Gromov's filling volume inequality for n-dimensional Lipschitz cycles (with integer and Z_2-coefficients) in -spaces.…