Banca de QUALIFICAÇÃO: VICTOR BENICIO VERGARA SEGURA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE : VICTOR BENICIO VERGARA SEGURA
Data: 25/09/2026
HORA: 15:00
LOCAL: Sala 303 do Bloco B do Campus de Santo André da Universidade Federal do ABC
TÍTULO:

Michael-Simon-type inequality for varifolds with Dini-controlled first variation

PÁGINAS: 151
RESUMO:

This thesis develops an intrinsic approach for the study of varifolds in Riemannian manifolds whose first variation satisfies a control condition of the Dini type. This condition quantitatively controls the stationarity deficit by a nondecreasing modulus ω, whose cumulative contribution is described by the amount of Dini Dω(R). Working directly with the Riemannian distance, the Levi-Civita connection and comparison estimates for the Hessian, we obtain a fundamental inequality of weighted monotonicity without going through an isometric immersion of the environment in a Euclidean space. As a consequence, we demonstrate the existence and upper semicontinuity of the density, as local estimates for the mass of the varifold. Under appropriate assumptions of density, local growth of mass and smallness of support of the function considered, we establish a local inequality of the Poincaré type. For dimensions m ≥ 2, we also prove an intrinsic inequality of the Michael–Simon-type, whose constant depends explicitly on the dimension, the local geometry of the manifold, the scale considered, and the accumulated quantity Dω(R). The variational framework used does not require that the first variation be locally represented by a Radon measure or by an integrable mean curvature vector. This distinction is illustrated by the construction of a graph C1,Dini whose associated varifold satisfies the Dini condition, but its first variation is not locally finite. Finally, we show that the classical hypotheses of the Allard type, with generalized mean curvature in Lp, p > m, imply the Dini condition considered in this thesis.

 

MEMBROS DA BANCA:
Presidente - Interno ao Programa - 1882430 - STEFANO NARDULLI
Membro Titular - Examinador(a) Interno ao Programa - 1067113 - DAHISY VALADAO DE SOUZA LIMA
Membro Titular - Examinador(a) Externo à Instituição - JOAO HENRIQUE SANTOS DE ANDRADE - USP
Membro Suplente - Examinador(a) Interno ao Programa - 3147167 - HENGAMEH RAEISIDEHKORDI
Membro Suplente - Examinador(a) Externo ao Programa - 2604830 - MARCIO FABIANO DA SILVA