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Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of to...
Magnitude is a real-valued invariant of metric spaces, analogous to the Euler characteristic
of topological spaces and the cardinality of sets. The denition of magnitude is a special case of a gener...
Systems of dyadic cubes in a doubling metric space
Space of homogeneous type dyadic cube random geometric construction
2011/1/20
A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to gene...
Asymptotics of ACH-Einstein metric
Partially integrable almost CR manifolds ACH metrics the Einstein equation
2010/12/9
We study the boundary asymptotics of asymptotically complex hyperbolic (ACH) solution of the Einstein equation in terms of the induced partially integrable almost CR structure T1,0 on the boundary. On...
Spaces of Type BLO on Non-homogeneous Metric Measure Spaces
upper doubling geometrically doubling RBLO(μ) maximal operator
2010/11/30
Let (X, d, μ) be a metric measure space and satisfy the so-called upper dou-bling condition and the geometrically doubling condition. In this paper, the authors introduce the space RBLO(μ) and prove t...
Comparison of exit moment spectra for extrinsic metric balls
Riemannian submanifolds extrinsic balls torsional rigidity L1-moment spectra
2010/12/1
We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn.