Banca de DEFESA: CARLOS HENRIQUE DA SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : CARLOS HENRIQUE DA SILVA
DATE: 26/08/2021
TIME: 14:00
LOCAL: Instituto de Matemática
TITLE:

Characterizations of hypersurfaces with constant r-mean curvature

KEY WORDS:

Embedded hypersurfaces; r-mean curvature; Compact hypersurfaces; Euclidean space; Open hemisphere; Hyperbolic space; Alexandrov theorem; Theorem of Montiel e Ros.

PAGES: 67
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:

This thesis aims to present a proof of a theorem of Sebastián Montiel and Antonio Ros which characterizes the compact hypersurfaces, without boundary, with constant r-mean curvature embedded in the space forms. This theorem generalizes the classical theorem of Alexandrov and states that

"The only compact, without boundary, hypersurfaces with constant r-mean curvature for some r=1,...,n, embedded in the Euclidean space, in the open hemisphere of the Euclidean sphere, or in the hyperbolic space, are the geodesic hyperspheres."

We remark that, despite we follow the ideas of Montiel and Ros, we give a new approach for some steps of the proof presented here.

BANKING MEMBERS:
Presidente - 2720885 - GREGÓRIO MANOEL DA SILVA NETO
Interno - 1119872 - HILARIO ALENCAR DA SILVA
Externo à Instituição - GREGORIO PACELLI FEITOSA BESSA - UFC