Banca de DEFESA: ALLAN KENEDY SANTOS SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : ALLAN KENEDY SANTOS SILVA
DATE: 31/03/2021
TIME: 14:00
LOCAL: Sala Virtual - Google Meet
TITLE:

Estimates of volume of minimal submanifolds in some symmetric spaces of rank one.

KEY WORDS:

Volume; Symetric spaces; Projective spaces;

PAGES: 62
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:

The theory of minimal surfaces came up with a problem proposed by Lagrange, which consisted

of the following: given a closed curve without self-intersections, find the surface of

smallest area that has that curve as boundary. Such a problem became known as

the Plateau Problem. It took about 16 years from Lagrange's work to discover non-trivial

examples of minimal surfaces due to Meusnier. The theory was stagnant for 60 years until

Scherk found new examples of minimal surfaces. With the work of Weierstrass it was possible to

obtain more examples of these surfaces. Thereafter there were major developments in theory,

becoming one of the most fertile fields of Differential Geometry. One class of problems studied

is that of estimate the volume of minimal submanifolds immersed in certain ambient

manifolds, such as spheres, hyperplanes, projective spaces, etc. The objective of the present

work is to provide lower bounds of volume of minimal compact submanifolds immersed

in certain symmetrical spaces of rank 1, namely: the unitary sphere Sn, and the real projective space RPn,

complex projective space CPn and quaternionic projective space HPn. It will be shown that if Mm is a

minimal submanifold of Sn, then volM >=V_c(n;M) where V_c(n;M) is the n-conformal volume

of M. Another estimate for this is volM>=c_n, where c_n = vol(Sn). In the case of

M being immersed in projective spaces, we have the lower bounds: c_n/2 in RPm, c_{n+1}/2\pi in

CPm and c_{n+2}=2\pi^2 in HPm.

BANKING MEMBERS:
Interno - 2474631 - MARCIO HENRIQUE BATISTA DA SILVA
Externo à Instituição - HENRIQUE FERNANDES DE LIMA - UFCG
Externo à Instituição - FÁBIO REIS DOS SANTOS - UFPE