Malliavin, Paul Formules de la moyenne, calcul de perturbations et théoremes d’annulation pour les formes harmoniques. (French) Zbl 0425.58022 J. Funct. Anal. 17, 274-291 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 44 Documents MSC: 58J65 Diffusion processes and stochastic analysis on manifolds 60J60 Diffusion processes 60J57 Multiplicative functionals and Markov processes 58A12 de Rham theory in global analysis 58A14 Hodge theory in global analysis Keywords:stochastic parallel displacement; Hodge-deRham Laplacian; Weitzenbock formula; Feynman-Kac formula; vanishing theorem for 1-forms; smallest eigenvalue of the Ricci tensor; harmonic forms Citations:Zbl 0241.60046 PDFBibTeX XMLCite \textit{P. Malliavin}, J. Funct. Anal. 17, 274--291 (1974; Zbl 0425.58022) Full Text: DOI References: [1] Bochner; Yano, Curvature and Betti Numbers (1953), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0051.39402 [2] Darling; Siegert, (Proc. Nat. Acad.. Proc. Nat. Acad., Washington (1956)), 525 [3] Eells; Elworthy, Stochastic Developpement, (Warwick Seminar (1970-1971)) · Zbl 0355.60053 [4] J. Eells and P. Malliavin; J. Eells and P. Malliavin [5] Ito, Stochastic parallel transport, (Internat. Congr. Math.. Internat. Congr. Math., Stockholm (1962)) [6] Kac, M., (Second Symposium of Probability (1952), Univ. California: Univ. California Berkeley, CA) [7] Malliavin, P., Géométrie Riemannienne stochastique, (Séminaire Jean Leray (1974), Collège de France) [8] Morrow; Kodaira, Complex Manifolds (1971), New York · Zbl 0325.32001 [9] Nijenhuis, Kon. Nederlandse Aka., 235 (1963) [10] Pinsky, Trans. Amer. Math. Soc., 167, 89-113 (1972) [11] de Rham, Variétés Différentiables (1956), Paris · Zbl 0065.32401 [12] Stroock, Comm. Pure Appl. Math., 23, 447-457 (1970) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.