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## On isoperimetric sets of radially symmetric measures

Contemporary Mathematics Series. 2011. Vol. 545. P. 123-154.

Kolesnikov A., Zhdanov R.

We study the isoperimetric problem for the radially symmetric measures. Applying the spherical symmetrization procedure and variational arguments we reduce this problem to a one-dimensional ODE of the second order. Solving numerically this ODE we get an empirical description of isoperimetric regions of the planar radially symmetric exponential power laws. We also prove some isoperimetric inequalities for the log-convex measures. It is shown, in particular, that the symmetric balls of large size are isoperimetric sets for strictly log-convex and radially symmetric measures. In addition, we establish some comparison results for general log-convex measures.

Research target:
Philosophy, Ethics, and Religious Studies

Language:
English

Turkensteen M., Ghosh D., Goldengorin B. I. et al., European Journal of Operational Research 2008 Vol. 189 No. 3 P. 775-788

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The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(ˆR, ˆ F) defined by a pair of compatible
solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the ...

Added: October 16, 2012

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family of commutative subalgebras, called the quantum shift of argument
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action on finite-dimensional modules is diagonalizable and their joint spectra
are in bijection with the set of monodromy-free opers for the Langlands dual ...

Added: October 12, 2012

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Added: October 12, 2012

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Modifications of bundles over complex curves is an operation that allows one to
construct a new bundle from a given one. Modifications can change a topological type of
bundle. We describe the topological type in terms of the characteristic classes of the bundle.Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. ...

Added: October 15, 2012

Feigin E., Fourier G., Littelmann P., International Mathematics Research Notices 2011 Vol. 2011 No. 24 P. 5760-5784

We study the PBW filtration on the highest weight representations V(λ) of sp2n. This
filtration is induced by the standard degree filtration on U(n−). We give a description
of the associated graded S(n−)-module gr V(λ) in terms of generators and relations. We
also construct a basis of gr V(λ). As an application we derive a graded combinatorial
formula for ...

Added: October 12, 2012

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Added: July 31, 2012

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The main goal of the article is to give the definition of algebraic stability that
would permit us to consider stability, not only for algebraic vector bundles or
torsion-free coherent sheaves, but for the abelian category of coherent sheaves or
for whatever abelian category. We present an axiomatic description of the algebraic
stability on an abelian category and prove ...

Added: October 16, 2012

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Added: October 12, 2012

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Marshakov A., Theoretical and Mathematical Physics 2011 Vol. 169 No. 3 P. 1704-1723

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Liviu O., Verbitsky M., International Mathematics Research Notices 2012 No. 4 P. 894-903

A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and ...

Added: October 24, 2012

Amerik E., Proceedings of the Edinburgh Mathematical Society 2011 Vol. 51 No. 1 P. 1-7

Added: October 15, 2012

Series C., Bufetov A. I., Mathematical Proceedings of the Cambridge Philosophical Society 2011 Vol. 151 No. 1 P. 145-159

We use Series' Markovian coding for words in Fuchsian groups and the
Bowen-Series coding of limit sets to prove an ergodic theorem for Cesaro averages of
spherical averages in a Fuchsian group. ...

Added: October 18, 2012

Alcaraz F. C., Pyatov P. N., Rittenberg V., Journal of Statistical Mechanics: Theory and Experiment 2008 Vol. P01006 P. 1-38

We consider the raise and peel model of a one-dimensional fluctuating interface in
the presence of an attractive wall. The model can also describe a pair annihilation
process in a disordered unquenched media with a source at one end of the system. For
the stationary states, several density profiles are studied usingMonte Carlo simulations. We point out a ...

Added: October 16, 2012

Marshakov A., Mironov A., Morozov A., Journal of High Energy Physics 2009 No. 11(048) P. 1-15

Added: October 18, 2012