caa a22 4500 445836695 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0760-z doi (NATIONALLICENCE)springer-10.1007/s00209-010-0760-z On a modified parabolic complex Monge-Ampère equation with applications [Elektronische Daten] [Albert Chau, Luen-Fai Tam] We study a modified parabolic complex Monge-Ampère type equation on a complete non-compact Kähler manifold. We prove a short time existence result and obtain basic estimates. Applying these results, we prove that under certain assumptions on a given real and closed (1,1) form Ω and initial Kähler metric g 0 on M, the modified Kähler-Ricci flow g′=−Ric+Ω has a long time solution converging to a complete Kähler metric such that Ric=Ω, which extends the result in Cao (Invent Math 81:359-372, 1985) to non-compact manifolds. We will also obtain a long time existence result for the Kähler-Ricci flow which generalizes a result (Chau etal. in Can J Math, to appear). Springer-Verlag, 2010 Non-compact Kähler-Einstein metrics nationallicence Kähler-Ricci flow nationallicence Parabolic Monge-Ampère equation nationallicence Chau Albert Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada aut Tam Luen-Fai Department of Mathematics, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, Hong Kong, China aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 777-800 0025-5874 269:3-4<777 2011 269 209 https://doi.org/10.1007/s00209-010-0760-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0760-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chau Albert Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada aut NATIONALLICENCE 700 1- Tam Luen-Fai Department of Mathematics, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, Hong Kong, China aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 777-800 0025-5874 269:3-4<777 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer