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

@article{Berndtsson2007,
abstract = {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 $e^\{-t\phi \}$ where $\phi $ is a nondegenerate Morse function.},
affiliation = {Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S-412 96 Göteborg, Sweden},
author = {Berndtsson, Bo},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {-estimates; Morse inequalities},
language = {eng},
number = {4},
pages = {773-797},
publisher = {Université Paul Sabatier, Toulouse},
title = {$L^2$-estimates for the $d$-equation and Witten’s proof of the Morse inequalities},
url = {http://eudml.org/doc/10069},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Berndtsson, Bo
TI - $L^2$-estimates for the $d$-equation and Witten’s proof of the Morse inequalities
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 4
SP - 773
EP - 797
AB - 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 $e^{-t\phi }$ where $\phi $ is a nondegenerate Morse function.
LA - eng
KW - -estimates; Morse inequalities
UR - http://eudml.org/doc/10069
ER -