On the evolution of a Hermitian metric by its Chern-Ricci form
We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kähler-Ricci flow if the initial metric is Kähler. We find the maximal existence time for the flow in terms of the ini...
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| Veröffentlicht in: | Journal of differential geometry 2015-01, Vol.99 (1), p.125-163 |
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| container_title | Journal of differential geometry |
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| creator | Tosatti, Valentino Weinkove, Ben |
| description | We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kähler-Ricci flow if the initial metric is Kähler.
We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern
class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampère equation on Hermitian manifolds. |
| doi_str_mv | 10.4310/jdg/1418345539 |
| format | Article |
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We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern
class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampère equation on Hermitian manifolds.</description><identifier>ISSN: 0022-040X</identifier><identifier>EISSN: 1945-743X</identifier><identifier>DOI: 10.4310/jdg/1418345539</identifier><language>eng</language><publisher>Lehigh University</publisher><ispartof>Journal of differential geometry, 2015-01, Vol.99 (1), p.125-163</ispartof><rights>Copyright 2015 Lehigh University</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-7a46cd1b218aa7a46527562d4b1410bac95f14e668f6a2da6c916bec9cbf56d13</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,777,781,882,922,4010,27904,27905,27906</link.rule.ids></links><search><creatorcontrib>Tosatti, Valentino</creatorcontrib><creatorcontrib>Weinkove, Ben</creatorcontrib><title>On the evolution of a Hermitian metric by its Chern-Ricci form</title><title>Journal of differential geometry</title><description>We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kähler-Ricci flow if the initial metric is Kähler.
We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern
class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampère equation on Hermitian manifolds.</description><issn>0022-040X</issn><issn>1945-743X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNpdkF1LwzAYhYMoWKe3XucPZMt32xtRim5CYSAOdlfSNHEpazPSTNi_t2NFwavDeeE8vDwAPBI854zgRdt8LQgnGeNCsPwKJCTnAqWcba9BgjGlCHO8vQV3w9BiTHhGswQ8rXsYdwaab78_Rud76C1UcGVC56JTPexMDE7D-gRdHGCxM6FHH05rB60P3T24sWo_mIcpZ2Dz9vpZrFC5Xr4XLyXSjMmIUsWlbkhNSabUuQiaCkkbXo8P41rpXFjCjZSZlYo2SuqcyNroXNdWyIawGXi-cA_Bt0ZHc9R711SH4DoVTpVXrio25XSdYvRR_fkYEfMLQgc_DMHY3zXB1Vng_8EPD_5kKg</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>Tosatti, Valentino</creator><creator>Weinkove, Ben</creator><general>Lehigh University</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150101</creationdate><title>On the evolution of a Hermitian metric by its Chern-Ricci form</title><author>Tosatti, Valentino ; Weinkove, Ben</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-7a46cd1b218aa7a46527562d4b1410bac95f14e668f6a2da6c916bec9cbf56d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tosatti, Valentino</creatorcontrib><creatorcontrib>Weinkove, Ben</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of differential geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tosatti, Valentino</au><au>Weinkove, Ben</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the evolution of a Hermitian metric by its Chern-Ricci form</atitle><jtitle>Journal of differential geometry</jtitle><date>2015-01-01</date><risdate>2015</risdate><volume>99</volume><issue>1</issue><spage>125</spage><epage>163</epage><pages>125-163</pages><issn>0022-040X</issn><eissn>1945-743X</eissn><abstract>We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kähler-Ricci flow if the initial metric is Kähler.
We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern
class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampère equation on Hermitian manifolds.</abstract><pub>Lehigh University</pub><doi>10.4310/jdg/1418345539</doi><tpages>39</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of differential geometry, 2015-01, Vol.99 (1), p.125-163 |
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| language | eng |
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| source | Project Euclid Complete |
| title | On the evolution of a Hermitian metric by its Chern-Ricci form |
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