Abstract
Let C and C′ be two smooth self-transverse immersions of S1 into ℝ2. Both C and C′ subdivide the plane into a number of disks and one unbounded component. An isotopy of the plane which takes C to C′ induces a one-to-one correspondence between the disks of C and C′. An obvious necessary condition for there to exist an area-preserving isotopy of the plane taking C to C′ is that there exists an isotopy for which the area of every disk of C equals that of the corresponding disk of C′. In this paper we show that this is also a sufficient condition.
Citation
Cecilia Karlsson. "Area-preserving isotopies of self-transverse immersions of S1 in ℝ2." Ark. Mat. 51 (1) 85 - 97, April 2013. https://doi.org/10.1007/s11512-012-0165-9
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