We will first give a rigorous proof of (S), and then investigate the family of sets such that equality holds true in Steiner inequality. De Giorgi: Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita.
Maggi: Sets of Finite Perimeter and Geometric Variational Problems: an Introduction to Geometric Measure Theory.
Students will be given support in the seminars on how to prepare, how to present and what is expected.
This page contains details for the topics available for final year dissertations for MMath students, and for projects for BSc students.
Key words: Isoperimetric Inequality, sets of finite perimeter.
We will give a rigorous proof of inequality (I), and we will consider interesting related problems. De Giorgi: Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita. Consider a collection of independent Bernoulli random variables ! Key words: probability metrics, rates of convergence, Bayesian inverse problems Recommended modules: Introduction to Probability, Measure and Integration. Key words: Sequence alignment, global alignment, optimality regions, multiple sequence alignments, algebraic statistics. The problem of regularity of these functions is widely open, at this time it is unknown whether they are differentiable everywhere if ! Miroslav Chlebik Presentation [PDF 309.98KB] Key words: Lipschitz mappings, optimal Lipschitz extension,degenerate elliptic PDEs, infinity harmonic functions. We examine various techniques to study pointwise behaviour of these functions. and Juutinen, P., A tour of the theory of absolutely minimizing functions, Bull. In order to give a rigorous meaning to inequality (I), one has to clarify what we mean by , which is a very useful tool in geometric variational problems. Maggi: Sets of Finite Perimeter and Geometric Variational Problems: an Introduction to Geometric Measure Theory. Steiner Symmetrization is a very simple and powerful technique in analysis, and has several remarkable applications to problems of geometric and functional nature. 10 hours of seminars and 3 hours of seminars in the MT. The ratio of lecture time and seminar time varies each week.Seminars do not include personal supervision time, which is scheduled independently with student supervisors. $$\begin \tag* P (E^S) \leq P(E) \quad \text E \subset \mathbb^n. , and (see, for instance, Theorem 14.4 in ) is satisfied: !