Grushin-harmonic functions are examples of solutions to degenerate elliptic equation, which share a lot of properties with standard harmonic functions (e.g. the strong maximum principle, the Harnack inequality). During the talk, I shall cover the main result from a paper by Xairong Liu and Xiaoping Yang Critical points and level sets of Grushin-harmonic functions in the plane (2021), which states that critical points of the before-mentioned functions are isolated and level sets at those points have similar geometry to level sets of harmonic functions at such points.

The main portion of the talk will be preceded by a short introduction to general Grushin-type spaces.

Meeting ID: 842 9950 2669 Passcode: 552370