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$L^{2}$ -estimates for the $d$ -equation and Witten’s proof of the Morse inequalities

Bo Berndtsson (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

This is an introduction to Witten’s analytic proof of the Morse inequalities. The text is directed primarily to readers whose main interest is in complex analysis, and the similarities to Hörmander’s $L^{2}$ -estimates for the $\bar{\partial}$ -equation is used as motivation. We also use the method to prove $L^{2}$ -estimates for the $d$ -equation with a weight $e^{- t φ}$ where $φ$ is a nondegenerate Morse function.

Landesman-Lazer type condition and nonlinearities with linear growth

Pavel Drábek (1990)

Czechoslovak Mathematical Journal

Large H-Surfaces Via the Mountain-Pass-Lemma.

Michael Struwe (1985)

Mathematische Annalen

Le problème inverse du calcul des variations

Michel Bauderon (1982)

Annales de l'I.H.P. Physique théorique

Least area Tori and 3-manifolds of nonnegative scalar curvature.

Mingliang Cai, G.J. Galloway (1996)

Mathematische Zeitschrift

Lefschetz theorems for the integral leaves of a holomorphic one-form

Carlos Simpson (1993)

Compositio Mathematica

Lemme de Morse et calcul des variations

P. Antoine (1979)

Mémoires de la Société Mathématique de France

Lepagean 2-forms in higher order Hamiltonian mechanics. I. Regularity

Olga Krupková (1986)

Archivum Mathematicum

Les travaux de Nabutovsky et Weinberger sur la complexité de l'espace des variétés riemanniennes

Laurent Bessières (2000/2001)

Séminaire de théorie spectrale et géométrie

Lewy's theorem fails in higher dimensions.

John C. Wood (1991)

Mathematica Scandinavica

Light rays in static spacetimes with critical asymptotic behavior: a variational approach.

Luisi, Valeria (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

L'indice de Morse dans le calcul variationnel

J. J. Duistermaat (1973/1974)

Séminaire Équations aux dérivées partielles (Polytechnique)

Linear Growth Harmonic Functions on Complete Manifolds with Nonnegative Ricci Curvature.

J. Cheeger, T.H. Colding (1995)

Geometric and functional analysis

Linear $\infty$ -harmonic maps between Riemannian manifolds.

Wang, Ze-Ping (2009)

Beiträge zur Algebra und Geometrie

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....

Currently displaying 1 – 20 of 35

Page 1 Next

Displaying 1 – 20 of 35

$L^{2}$ -estimates for the $d$ -equation and Witten’s proof of the Morse inequalities

Landesman-Lazer type condition and nonlinearities with linear growth

Large H-Surfaces Via the Mountain-Pass-Lemma.

Le problème inverse du calcul des variations

Least area Tori and 3-manifolds of nonnegative scalar curvature.

Lefschetz theorems for the integral leaves of a holomorphic one-form

Lemme de Morse et calcul des variations

Lepagean 2-forms in higher order Hamiltonian mechanics. I. Regularity

Les travaux de Nabutovsky et Weinberger sur la complexité de l'espace des variétés riemanniennes

Lewy's theorem fails in higher dimensions.

Light rays in static spacetimes with critical asymptotic behavior: a variational approach.

L'indice de Morse dans le calcul variationnel

Linear Growth Harmonic Functions on Complete Manifolds with Nonnegative Ricci Curvature.

Linear $\infty$ -harmonic maps between Riemannian manifolds.

Linking and the Morse complex

Linking method for periodic non-autonomous fourth-order differential equations with superquadratic potentials.

Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity

Liouville theorem for harmonic maps with potential.

Liouville theorems for exponentially harmonic functions on Riemannian manifolds.

Liouville theorems for harmonic maps.

Currently displaying 1 – 20 of 35