Area and Coarea formulas in Geometric Measure Theory

Postgraduate Thesis uoadl:2775280 404 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2018-06-22
Year:
2018
Author:
Gkegkios Alexios
Supervisors info:
Τηλέμαχος Χατζηαφράτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Οι τύποι Area και Coarea στη Γεωμετρική Θεωρία Μέτρου
Languages:
Greek
Translated title:
Area and Coarea formulas in Geometric Measure Theory
Summary:
In this master thesis we present and prove Area and Coarea formulas.
In introductory Chapter 1 the two formulas are stated along with representative examples. The wider proof procedure starts from Chapter 2 where the necessary background about Measure Theory is propounded. In Chapter 3 Hausdorff measures are introduced. Chapter 4 contains information regarding Lipschitz functions. Here we prove Rademacher's Theorem. Chapter 5 includes some basic linear algebra followed by more specific tools. In Chapter 6 we finally prove Area and Coarea formulas.
Main subject category:
Science
Keywords:
Area, Coarea, Geometric Measure Theory
Index:
No
Number of index pages:
2
Contains images:
Yes
Number of references:
9
Number of pages:
85
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