On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces

Autor(es)

Barreto, Alexandre Paiva ; Fontenele, Francisco ; Hartmann, Luiz

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS; v. N/A, p. 8-pg., 2021-09-06.

Resumo

We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space Rn+1, n >= 2, defined by polynomials of odd degree. Also we prove that the hyperspheres and the round cylinders are the only regular algebraic hypersurfaces with non-zero constant mean curvature in Rn+1, n >= 2, defined by polynomials of degree less than or equal to three. These results give partial answers to a question raised by Barbosa and do Carmo. (AU)

• Processo FAPESP: 18/23202-1 - Invariantes espectrais em pseudovariedades
• Beneficiário: Luiz Roberto Hartmann Junior
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/03721-4 - Superfícies de Weingarten, Self-Shrinkers e Superfícies Hiperbólicas
• Beneficiário: Alexandre Paiva Barreto
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/20854-0 - Superfícies de Weingarten em R^3 e hipersuperfícies completas com curvatura de Ricci negativa em R^{n+1}
• Beneficiário: Alexandre Paiva Barreto
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil