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On the area-preserving Domain-Straightening Theorem
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Abstract(s)
O clássico teorema da retificação do domínio no plano garante que, sob determinadas condições de não degeneracidade da derivada da função f : R^2 ---> R num ponto p existem abertos U e V de R2, p \in V e um difeomorfismo h: U ---> V tal que foh tem todas as suas curvas de nível em h−1(V ) contidas em retas. Provamos que tal deformação h pode ser feita preservando a área.
The classical Domain-Straightening Theorem on the plane says that under a non-degeneracy condition on the derivative of a map f : R 2 → R in a point p there exists a neighborhood V ⊂ R 2 of p, U ⊂ R 2 and a diffeomorphism h: U → V such that f ◦ h has all level curves in h −1 (V) defined by straight lines. We prove that such deformation h can be made area-preserving.
The classical Domain-Straightening Theorem on the plane says that under a non-degeneracy condition on the derivative of a map f : R 2 → R in a point p there exists a neighborhood V ⊂ R 2 of p, U ⊂ R 2 and a diffeomorphism h: U → V such that f ◦ h has all level curves in h −1 (V) defined by straight lines. We prove that such deformation h can be made area-preserving.
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Keywords
Teorema da retificação do domínio Fluxos que preservam a área Teoremas de caixa de fluxo Domain-Straightening Theorem Area-preserving flows Flowbox theorems
Citation
M. Bessa, P. Morais, On the area-preserving Domain-Straightening Theorem, Boletim da Sociedade Portuguesa de Matemática, 79, 2021
Publisher
Sociedade Portuguesa de Matemática (SPM)