Banca de DEFESA: Hector Andrés Rosero García

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Hector Andrés Rosero García
DATE: 31/05/2023
TIME: 14:00
LOCAL: Departamento de Matemática
TITLE:

Ends of complete gradient ρ−Einstein solitons

KEY WORDS:

gradient ρ−Einstein solitons, ends, parabolicity, connectedness at infinity

PAGES: 90
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In this thesis we consider ends of complete gradient ρ−Einstein solitons by adapting and extending the techniques used to describe ends of Ricci solitons. For shrinking Schouten solitons we show that there is at most one f-non-parabolic end, where f stands for the potential function. Also, under an appropriate bound on the scalar curvature, we show that all ends of a shrinking Schouten soliton are non-parabolic. With no additional assumptions, we show that an expanding Schouten soliton must be connected at infinity, that is, it has only one end, unless it is a rigid Ricci soliton. Regarding ρ−Einstein solitons with ρ [0, ), we provide bounds on the scalar curvature for a shrinking soliton to be connected at infinity.

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