Banca de DEFESA: FRANCISCO CLEONE NERES DE LIMA
Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.STUDENT : FRANCISCO CLEONE NERES DE LIMA
DATE: 30/03/2021
TIME: 10:00
LOCAL: Sala virtual no Google Meet
TITLE:
ESTIMATING THE FIRST EIGENVALUE OF THE LAPLACIAN IN MINIMAL HYPERSURFACES
KEY WORDS:
First eigenvalue; Laplacian; Minimal hypersurface; Reilly's formula; Bochner's formula; Ricci curvature.
PAGES: 46
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:
In the article "A first eigenvalue estimate for minimal hypersurfaces" H. Choi e A. N. Wang obtained a lower bound for the first eigenvalue of the Laplacian of a compact orientable embedded minimal hypersurface in an compact orientable manifold with Positive Ricci curvature. In this dissertation, using covering space argument we prove this result dropping the orientability assumption. Moreover, we use Reilly's Formula was used, which is actually a version obtained by integrating of Bochner's Formula. Combining Choi and Wang's estimate with Yang and Yau's Theorem, we found a upper bounds estimate for the area of an embedded minimal surface in S3 only depending on its topology, more precisely only in terms of the genus of the surface.
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