Smooth area preserving isotopies of self transverse immersions of S¹ into R²
Let C and C′ be two smooth self transverse immersions of S1 into R2. BothC and C′ divide the plane into a number of disks and one unbounded component.An isotopy of the plane which takes C to C′ induces a 1-1 correspondence betweenthe disks of C and C′. An obvious necessary condition for there to exi...
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| Format: | Others |
| Language: | English |
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Uppsala universitet, Matematiska institutionen
2009
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| Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-112522 |
| Summary: | Let C and C′ be two smooth self transverse immersions of S1 into R2. BothC and C′ divide the plane into a number of disks and one unbounded component.An isotopy of the plane which takes C to C′ induces a 1-1 correspondence betweenthe disks of C and C′. An obvious necessary condition for there to exist an areapreserving isotopy of the plane taking C to C′ is that there exists an isotopy forwhich the area of every disk of C has the same area as the corresponding disk ofC′. In this paper we show that this is also a sufficient condition. |
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