Stability of isoperimetric type inequalities for some Monge–Ampère functionals |
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Authors: | Daria Ghilli Paolo Salani |
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Institution: | 1. Dipartimento di Matematica, “U. Dini”, viale Morgagni 67/A, 50134, Firenze, Italy
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Abstract: | We investigate the stability of some inequalities of isoperimetric type related to Monge–Ampère functionals. In particular, firstly we prove the stability of a reverse Faber–Krahn inequality for the Monge–Ampère eigenvalue and its generalization. Then we give a stability result for the Brunn–Minkowski inequality and for a consequent Urysohn’s type inequality for the so-called \(n\) -torsional rigidity, a natural extension of the usual torsional rigidity. |
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