Pontryagin’s Maximum Principle for the Loewner Equation in Higher Dimensions

Roth, Oliver

Canadian journal of mathematics, Tome 67 (2015) no. 4, pp. 942-960

Résumé

In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin’s maximum principle from optimal control theory for the Loewner equation in several complex variables. Based on recent work of Arosio, Bracci, andWold, we then apply our version of the Pontryagin maximum principle to obtain first-order necessaryconditions for the extremal mappings for a wide class of extremal problems over the set of normalizedbiholomorphic mappings on the unit ball in ${{\mathbb{C}}^{n}}$ .

Détail

DOI : 10.4153/CJM-2014-027-6

Mots-clés : 32H02, 30C55, 49K15, Univalent functions, Loewner’s equation

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