On Isoperimetric Property of Two-dimensional Manifolds with Curvature Bounded from Above by K

Yu. G. Reshetnyak(deceased) ()
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Yu. G. Reshetnyak(deceased): Sobolev Institute of Mathematics

Chapter Chapter 9 in Reshetnyak's Theory of Subharmonic Metrics, 2023, pp 229-250 from Springer

Abstract: Abstract Let M be an arbitrary domain in the plane of complex variable z = x + iy and let λ(z) = λ(x, y) ≥ 0 be a Borel measurable function defined over M such that for each open set G ⊂ M σ λ ( G ) = ∬ G λ ( z ) d x d y > 0 . $$\displaystyle \sigma _\lambda (G)=\iint _G \lambda (z) \mathrm{d} x \mathrm{d} y >0~. $$ We use the following notation: σ λ ( z 0 , r ) = ∬ | z − z 0 | 0 such that for z0 ∈ F and r

Date: 2023
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DOI: 10.1007/978-3-031-24255-7_9

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