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Browsing by Subject "Geometric measure theory"

Browsing by Subject "Geometric measure theory"

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  • A criterion for N- rectifiable sets 
    Al Kadi, Monica (Notre Dame University-Louaize, 2019)
    Geometric measure theory was developed in the second half of the 20th century to manipulate the structure and regularity questions in the calculus of variations. The main goal of this thesis is to introduce the theory of " rectifiability of sets". Rectifiable sets are considered smooth in a certain measure theoretic sense. Rectifiable sets are basic concepts in geometric measure theory. Their theory began with the study and determination of length, area or volume of sets in Euclidean space. Rectifiable sets have many of the desirable properties that smooth sets have. In this thesis, we will ...
  • A criterion for sets of locally finite perimeter 
    Bou Kaed Bey, Heba Badri (Notre Dame University-Louaize, 2019)
    Geometric measure theory could be described as differential geometry, generalized through measure theory to deal with maps and surfaces that are not necessarily smooth, and applied to the calculus of variations. Geometric measure theory is important because it studies sets, their variation and their boundaries (from the measure theoretic sense). In particular, a very interesting branch in Geometric measure theory, is the sets of locally finite perimeter. Just as their name actually shows, these sets are essentially sets whose perimeter is (locally) finite. In this thesis we start by giving a ...