Banca de QUALIFICAÇÃO: MARCOS AGNOLETTO FORTE

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE : MARCOS AGNOLETTO FORTE
DATA : 18/09/2025
HORA: 14:00
LOCAL: Sala 406 do Bloco B do Campus de Santo André da Universidade Federal do ABC
TÍTULO:

ON THE REGULARITY THEORY OF GENERALIZED SURFACES

PÁGINAS: 7
RESUMO:

In this Ph.D. thesis proposal, we study the regularity of energy-minimizing geometric structures within the framework of Geometric Measure Theory (GMT), which extends classical minimal surface theory to generalized objects such as varifolds. We establish an interior epsilon regularity theorem for varifolds in Alexandrov spaces with positive lower bounds on the injectivity radius and double-sided bounds on sectional curvature showing that, near regular points, the support can be represented as a $\mathcal{C}^{1,\alpha}$ graph, where $0 < \alpha < 1$, and that the regular set is relatively open and dense.

Our current work follows the line of research developed by Prof. Camillo De Lellis, which itself builds upon the foundational techniques of Frederick Almgren Jr. for studying the interior regularity of minimizing currents. Within this framework, we also address regularity problems for $\left(Q - \frac{1}{2}\right)$ Dirichlet minimizers, which naturally arise in the regularity theory of higher-codimension currents.

MEMBROS DA BANCA:
Membro Titular - Examinador(a) Interno ao Programa - 054.604.516-20 - MARCUS ANTONIO MENDONCA MARROCOS - UFAM
Membro Titular - Examinador(a) Interno ao Programa - 3389558 - VINICIUS COLFERAI CORREA MIRANDA
Presidente - Externo ao Programa - 2604830 - MARCIO FABIANO DA SILVA
Membro Suplente - Examinador(a) Interno ao Programa - 1882430 - STEFANO NARDULLI
Membro Suplente - Examinador(a) Externo ao Programa - 1734928 - SINUE DAYAN BARBERO LODOVICI