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The tangential Kohn Laplacian via conformal equivalence

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In a recent preprint, Jih-Hsin Cheng, Andrea Malchiodi and Paul Yang have formulated a positive mass theorem in 3-dimensional CR geometry, and reduced its proof to the solution of a tangential Kohn Laplacian on a special class of non-compact strongly pseudoconvex CR manifolds. In joint work with Chin-Yu Hsiao, we established the solution of such Kohn Laplacians, thereby completing their program. We will survey some of these developments in this talk, and highlight the role of conformal equivalence in this regard. Attempts will be made to make the talk self-contained.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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