{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T22:29:42Z","timestamp":1787005782721,"version":"build-2736575974"},"reference-count":0,"publisher":"National Academy of Sciences","issue":"2","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[1974,2]]},"abstract":"<jats:p>\n                    Quantitative estimates are obtained by comparison with ordinary differential equations associated to a subharmonic exhaustion function\n                    <jats:italic>q<\/jats:italic>\n                    . We associate with\n                    <jats:italic>q<\/jats:italic>\n                    a ratio\n                    <jats:italic>a<\/jats:italic>\n                    , which can be considered as the heat flow in an intrinsic time, and the sup and the inf of\n                    <jats:italic>a<\/jats:italic>\n                    , namely\n                    <jats:italic>a<\/jats:italic>\n                    <jats:sup>+<\/jats:sup>\n                    and\n                    <jats:italic>a<\/jats:italic>\n                    <jats:sup>-<\/jats:sup>\n                    , on the level hypersurfaces of\n                    <jats:italic>q<\/jats:italic>\n                    . Then\n                    <jats:italic>a<\/jats:italic>\n                    <jats:sup>+<\/jats:sup>\n                    and\n                    <jats:italic>a<\/jats:italic>\n                    <jats:sup>-<\/jats:sup>\n                    define heat flows on the real line. Comparison between the heat flow on the manifold and heat flows on the line are obtained by stochastic integrals.\n                  <\/jats:p>","DOI":"10.1073\/pnas.71.2.381","type":"journal-article","created":{"date-parts":[[2006,5,31]],"date-time":"2006-05-31T02:53:33Z","timestamp":1149044013000},"page":"381-383","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":17,"title":["Asymptotic of the Green's Function of a Riemannian Manifold and Ito's Stochastic Integrals"],"prefix":"10.1073","volume":"71","author":[{"given":"Paul","family":"Malliavin","sequence":"first","affiliation":[{"name":"Institut Henri Poincar\u00e9, 11 rue Pierre et Marie Curie, Paris 75005, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[1974,2]]},"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.71.2.381","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T10:27:01Z","timestamp":1649845621000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/full\/10.1073\/pnas.71.2.381"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,2]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1974,2]]}},"alternative-id":["10.1073\/pnas.71.2.381"],"URL":"https:\/\/doi.org\/10.1073\/pnas.71.2.381","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[1974,2]]},"assertion":[{"value":"1974-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}