TITLE: PDE on manifolds
QUESTION [18 upvotes]: I am currently in a PDE course where one of the requirements is to present a paper in PDE. I am wondering if anyone can suggest an early (read foundational, first introductory) paper talking about PDE on manifolds. I am a topologist (homotopy theorist) by training so i prefer things to be coordinate free, but this may not be possible. For example something relating various notions of curvature to PDE, or something on viewing the PDE globally in terms of acting on sections would be great.
If this isn't the best forum my apologies.

REPLY [2 votes]: All previous replies have their own merit, however I am surprised not to find the first thing that popped in my head: That Frobenius' theorem concerning the integrability of a differential system on the tangent bundle. And maybe as a homotopy-oriented researcher (kudos to that) you could relate a simple result and use it as an intro to the Atiyah-Singer index theorem.
Or maybe not. Frobenius' theorem is pretty enough to hold the show on its own.