All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 9 Next

Displaying 161 – 180 of 241

Showing per page

Linking and the Morse complex

Michael Usher (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

For a Morse function f on a compact oriented manifold M , we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial linking number, such that the minimal value of f on one of the components is larger than its maximal value on the other. Indeed we characterize the precise number of critical points of f in terms of the Betti numbers of M and the behavior of f with respect to links....

Liouville theorems for self-similar solutions of heat flows

Jiayu Li, Meng Wang (2009)

Journal of the European Mathematical Society

Let N be a compact Riemannian manifold. A quasi-harmonic sphere on N is a harmonic map from ( ℝ m , e | x | 2 / 2 ( m - 2 ) / d s 0 2 ) to N ( m ≥ 3 ) with finite energy ([LnW]). Here d s 2 0 is the Euclidean metric in ℝ m . Such maps arise from the blow-up analysis of the heat flow at a singular point. In this paper, we prove some kinds of Liouville theorems for the quasi-harmonic spheres. It is clear that the Liouville theorems imply the existence of the heat flow to the target N . We also derive gradient estimates and Liouville theorems for positive...

Liouville type theorems for φ-subharmonic functions.

Marco Rigoli, Alberto G. Setti (2001)

Revista Matemática Iberoamericana

In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.

Currently displaying 161 – 180 of 241