Global Inversion via the Palais-smale Condition
نویسندگان
چکیده
Fixing a complete Riemannian metric g on Rn, we show that a local diffeomorphism f : Rn → Rn is bijective if the height function f · v (standard inner product) satisfies the Palais-Smale condition relative to g for each for each nonzero v ∈ Rn. Our method substantially improves a global inverse function theorem of Hadamard. In the context of polynomial maps, we obtain new criteria for invertibility in terms of Lojasiewicz exponents and tameness of polynomials.
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