University of Jyvaskyla in Finland

Part 3: The isoperimetric inequality. Stability and related topics

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B1 L4 R4102

The aim of the course is to give a self contained introduction, at the level of a graduate course, to the stability of the isoperimetric inequality and other related geometric and functional inequality such as the Sobolev inequality, the Faber-Krahn and the Brunn-Minkowski inequality. Lecture 3: I will present Fuglede’s proof of the quantitative isoperimetric inequality for convex and for nearly spherical sets

Part 1: The isoperimetric inequality. Stability and related topics

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B1 L4 R4102

The aim of the course is to give a self contained introduction, at the level of a graduate course, to the stability of the isoperimetric inequality and other related geometric and functional inequality such as the Sobolev inequality, the Faber-Krahn and the Brunn-Minkowski inequality. Lecture 1: I will introduce some basic notions of the theory of sets of ignite perimeter and of geometric measure theory.

Part 2: The isoperimetric inequality. Stability and related topics

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B1 L4 R4102

The aim of the course is to give a self contained introduction, at the level of a graduate course, to the stability of the isoperimetric inequality and other related geometric and functional inequality such as the Sobolev inequality, the Faber-Krahn and the Brunn-Minkowski inequality. Lecture 2: I will present De Giorgi’s proof of the isoperimetric inequality and comment on other proofs of the isoperimetric inequality

Part 4: The isoperimetric inequality. Stability and related topics

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B1 L4 R4102

The aim of the course is to give a self contained introduction, at the level of a graduate course, to the stability of the isoperimetric inequality and other related geometric and functional inequality such as the Sobolev inequality, the Faber-Krahn and the Brunn-Minkowski inequality. Lecture 4: I will discuss the quantitative isoperimetric inequality in the general case and the quantitative form of related geometric and functional inequalities.