Arşiv ve Dokümantasyon Merkezi
Dijital Arşivi

On a volume estimate for some subsets of a Grassmannian

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dc.contributor Graduate Program in Mathematics.
dc.contributor.advisor Eden, Alp,
dc.contributor.author Demirkaya, Emre.
dc.date.accessioned 2023-03-16T11:21:39Z
dc.date.available 2023-03-16T11:21:39Z
dc.date.issued 2013.
dc.identifier.other MATH 2013 D46
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/15269
dc.description.abstract Measure theory gives us a technique for proving existence theorems. In simple terms this technique can be described as follows: start with a set and put a measure on it. Then nd the exact measure of a speci ed set A. By showing the set of elements B in A that do not satisfy a certain condition P has measure strictly smaller than the measure of the ambient set A, one can deduce the existence of elements in A that satis es the desired property P. This line of argument can only work when we have methods to nd the measure of the set A and also estimate from above the measure of B. This thesis is about one such argument introduced by Ben-Artzi et al. and utilized later successfully by Foias and Olson to prove the existence of a Mane's projection whose inverse is Holder continuous. The key estimate in those works was an inequality from integral geometry due to Santalo for measures of some subsets of the Grassmannian Space. The aim of this thesis is to expose and improve an alternate argument given by Friz and Robinson where they avoid working on the Grassmannian space and introduce the measures and estimates on a larger space while keeping track of the sizes of the coefficients.
dc.format.extent 30 cm.
dc.publisher Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013.
dc.subject.lcsh Grassmann manifolds.
dc.title On a volume estimate for some subsets of a Grassmannian
dc.format.pages ix, 50 leaves ;


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