Armeniakos, S. (2024, April 18). Isoperimetry for log-concave measures in the Euclidean Space [Presentation]. privatissimum of the research units for Convex and Discrete Geometry and Geometric Analysis, Wien, Austria.
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Date (published):
18-Apr-2024
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Event name:
privatissimum of the research units for Convex and Discrete Geometry and Geometric Analysis
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Event date:
18-Apr-2024
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Event place:
Wien, Austria
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Keywords:
Metric space; convex geometry
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Abstract:
For a metric measure space and a probability measure μ we can define the
Minkowski content of a measurable set as:
μ+(A) = lim inf
s→0+
μ(As) − μ(A)
s
.
For such a space we can define the isoperimetric profile in accordance with
the classical isoperimetric profile through:
Iμ(t) = inf{μ+(A) : ABorel, μ(A) = t}
An equivalent formulation of the so called Kannan - Lovasz - Simmonovits
conjecture, is that the isoperimetric profile is bounded from below by a constant
independent of the dimension for log-concave measures in Rd .
In this talk, we will present shortly the main results towards the proof of
this conjecture, and we will prove that the concture holds up to a polylog.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
