\(L^2\)-estimates for the \(d\)-equation and Witten's proof of the Morse inequalities

DOI10.5802/afst.1166zbMath1176.58009OpenAlexW2140535483MaRDI QIDQ954077

Bo Berndtsson

Publication date: 7 November 2008

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2007_6_16_4_773_0

zbMATH Keywords

Morse inequalities\(L^2\)-estimates

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Convexity of real functions in one variable, generalizations (26A51) Other analytical inequalities (26D20)

Related Items (5)

Levi problem in complex manifolds ⋮ On the Poincaré-Lelong equation in ℂⁿ ⋮ Characterizations of curvature positivity of Riemannian vector bundles and convexity or pseudoconvexity of bounded domains in \(\mathbb{R}^n\) or \(\mathbb{C}^n\) in terms of \(L^2\)-estimate of \(d\) or \(\overline{\partial}\) equation ⋮ Cauchy–Riemann meet Monge–Ampère ⋮ A right inverse of differential operator \(\frac{d^k}{dx^k} + a\) in weighted Hilbert space \(L^2(\mathbb{R}, e^{- x^2})\)

Cites Work

• Bergman kernels and local holomorphic Morse inequalities
• Supersymmetry and Morse theory
• Semi-classical analysis for the Schrödinger operator and applications
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
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