Weak solutions to degenerate complex Monge–Ampère flows II
Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for dege...
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| Published in | Advances in mathematics (New York. 1965) Vol. 293; pp. 37 - 80 |
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| Format | Journal Article |
| Language | English |
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30.04.2016
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| ISSN | 0001-8708 1090-2082 1090-2082 |
| DOI | 10.1016/j.aim.2016.02.010 |
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| Abstract | Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations.
The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge–Ampère flows on compact Kähler manifolds. Our general theory allows in particular to define and study the (normalized) Kähler–Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian. |
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| AbstractList | Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations.
The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge–Ampère flows on compact Kähler manifolds. Our general theory allows in particular to define and study the (normalized) Kähler–Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian. |
| Author | Eyssidieux, Philippe Zeriahi, Ahmed Guedj, Vincent |
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| Keywords | Kähler–Ricci flow Canonical singularities Complex Monge–Ampère flows Viscosity solutions |
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| StartPage | 37 |
| SubjectTerms | Canonical singularities Complex Monge–Ampère flows Complex Variables Differential Geometry Kähler–Ricci flow Mathematics Viscosity solutions |
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| Title | Weak solutions to degenerate complex Monge–Ampère flows II |
| URI | https://dx.doi.org/10.1016/j.aim.2016.02.010 https://hal.science/hal-01656933 https://doi.org/10.1016/j.aim.2016.02.010 |
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