Open and surjective mapping theorems for differentiable maps with critical points

DOI10.14321/realanalexch.46.1.0107zbMath1483.26012OpenAlexW4293509628WikidataQ113743901 ScholiaQ113743901MaRDI QIDQ2054552

Liangpan Li

Publication date: 3 December 2021

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Open-and-surjective-mapping-theorems-for-differentiable-maps-with-critical/10.14321/realanalexch.46.1.0107.full

zbMATH Keywords

critical pointpolyanalytic functionopen mapsurjective mapdifferentiable map

Mathematics Subject Classification ID

Continuity and differentiation questions (26B05) Implicit function theorems, Jacobians, transformations with several variables (26B10) Other generalizations of analytic functions (including abstract-valued functions) (30G30)

Related Items (2)

New inverse and implicit function theorems for differentiable maps with isolated critical points ⋮ Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

Cites Work

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• Complex analysis I: Entire and meromorphic functions, polyanalytic functions and their generalizations. Transl. from the Russian by V. I. Rublinetskij and V. A. Tkachenko
• Fundamental Theorem of Algebra -- Yet Another Proof
• The inverse function theorem of Nash and Moser
• On the Surjectivity of Smooth Maps into Euclidean Spaces and the Fundamental Theorem of Algebra
• Local inversion for differentiable functions and the Darboux property
• A sufficient condition for locally open polyanalytic functions
• Local inversion theorems without assuming continuous differentiability

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