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Soon I will be learning curve shortening flow and I am under the impression that a knowledge of PDEs is essential. Specifically, what from PDEs is required?

For example, I plan on brushing up using the Evans' book on PDEs. Specifically, the heat equation in chapter 2, Sobolev spaces in chapter 5 and also calculus of variations in chapter 8. Is there anything else that would be necessary?

For reference, here is the contents page in the Evans' book on PDEs: https://bookstore.ams.org/gsm-19-r/13

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    $\begingroup$ My suggestion is to just start learning about the curve shortening flow and consult references, such as Evans' book, when needed. Mostly, you should be able to assume the general PDE theorems and focus on the arguments specific to curve-shortening. $\endgroup$ – Deane Yang Apr 14 '18 at 0:15

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