By using Minkowski addition of convex functions, we prove convexity and rearrangement properties of solutions to some Hessian equations in $R^3$ and Brunn–Minkowski and isoperimetric inequalities for related functionals.
Convexity of solutions and Brunn–Minkowski inequalities for Hessian equations in R^3 / P. Salani. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 229:(2012), pp. 1924-1948. [10.1016/j.aim.2011.12.009]
Convexity of solutions and Brunn–Minkowski inequalities for Hessian equations in R^3
SALANI, PAOLO
2012
Abstract
By using Minkowski addition of convex functions, we prove convexity and rearrangement properties of solutions to some Hessian equations in $R^3$ and Brunn–Minkowski and isoperimetric inequalities for related functionals.
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