I am aware that there is a nice result where one uses curve shortening flow to prove the isoperimetric inequality on the Euclidean plane, but could not seem to find the original article where this was done and was wondering if someone could point me towards this? I believe it was first done by Gage?



Proof of Isoperimetric Inequality using Curve Shortening Flow
The final paper:
Grayson, Matthew A.(1-UCSD)
*Shortening embedded curves.*
**Ann. of Math.** (2) 129 (1989), no. 1, 71–111. 


using results from:


Gage, Michael E.(1-CWR)
*An isoperimetric inequality with applications to curve shortening.*
**Duke Math. J.** 50 (1983), no. 4, 1225–1229. 


Gage, M. E.(1-CWR)
*Curve shortening makes convex curves circular.*
**Invent. Math.** 76 (1984), no. 2, 357–364. 


Gage, M.(1-RCT); Hamilton, R. S.(1-UCSD)
*The heat equation shrinking convex plane curves.*
**J. Differential Geom.** 23 (1986), no. 1, 69–96. 


Grayson, Matthew A.(1-UCSD)
*The heat equation shrinks embedded plane curves to round points.*
**J. Differential Geom.** 26 (1987), no. 2, 285–314. 


