Abstract
AbstractIn this chapter, we will establish that a non-constant equi-dimensional rational sphere map is a ball automorphism when \(n\ge 2\). The proof of this simple sounding result requires some geometric information which we gather. We will discuss the rudiments of CR geometry, including the Levi form and strong pseudoconvexity. We will encounter an unbounded realization of the unit sphere, the Heisenberg group, and an algebraic variety Xf associated with a rational sphere map f. We move even further from the unit sphere by stating and using some results by Baouendi-Rothschild and Baouendi-Huang-Rothschild on complex analogues of the Hopf lemma.
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