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Geometric Measure Theory I SemesterWiSe 2024 / 25 Lecturer Tim Laux Type of course (Veranstaltungsart) Vorlesung German title Geometrische Maßtheorie I Contents In the graduate-level course Geometric Measure Theory 1 we will study sets of finite perimeter which appear in many geometric problems as they generalize in a natural measure theoretic way the notion of sets with smooth boundaries and enjoy excellent compactness properties. After paving our way to defining sets of finite perimeter, we will study their compactness, structure, and regularity properties. If time permits, we will discuss further topics like minimal clusters, free discontinuity problems, and some applications. Literature Maggi, Francesco. Sets of finite perimeter and geometric variational problems: an introduction to Geometric Measure Theory. No. 135. Cambridge University Press, 2012. L. Craig Evans and Ronald F. Gariepy. Measure theory and fine properties of functions. Chapman and Hall/CRC, 2015. Luigi Ambrosio, Nicola Fusco, and Diego Pallara. Functions of bounded variation and free discontinuity problems. Vol. 254. Oxford: Clarendon Press, 2000. Recommended previous knowledge Working knowledge in measure theory and analysis is assumed. (The basic training in analysis is sufficient; Functional Analysis is useful but not necessary.) Time/Date Th, Fr: 8:15-10:00 Location M104 Registration
BV, MV, MGAGeo, MAngAn ECTS 9 |