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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of...
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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group
We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.
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Isoperimetric Clusters in Homogeneous Spaces via Concentration Compactness
We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in...
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Compactness of harmonic maps of surfaces with regular nodes
In this paper, we formulate and prove a general compactness theorem for harmonic maps of Riemann surfaces using Deligne–Mumford moduli space and...
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Compactness theory of the space of Super Ricci flows
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of...
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Compactness and fractal dimensions of inhomogeneous continuum random trees
We introduce a new stick-breaking construction for inhomogeneous continuum random trees. This new construction allows us to prove the necessary and...
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Dualities, Measure Concentration and Transportation
In these three lectures we shall review and discuss in detail the fascinating connection between duality transforms (mainly Legendre and polarity,...
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Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonnegative scalar curvature and some additional...
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Concentration breaking on two optimization problems
In the present paper, we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains,...
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Concentration of measure for classical Lie groups
We study the concentration of measure in metric-measurable (mm)-spaces. We define the notion of concentration locus of a flag sequence of...
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Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups....
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On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces
We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian stationary Lagrangian surfaces with bounded areas and Willmore...
