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Geometry Colloquium
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2013/11/28
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Shinichiroh MATSUO (Osaka University)
The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)
Shinichiroh MATSUO (Osaka University)
The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)
[ Abstract ]
In this talk I will talk about the modified Kazdan-Warner problem.
Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.
I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.
In this talk I will talk about the modified Kazdan-Warner problem.
Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.
I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.
