Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives

By I. Chavel. 2001

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Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs (2000, background): “5) has a well-known discrete analogue (see, for example [5], [10], [29], [32]).”
Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions (2007, unknown): “See the nice books of Chavel [19, 20] for more on these topics.”
H1 and BMO for certain locally doubling metric measures spaces (2009, background): “It is well known that Cheeger’s isoperimetric inequality for smooth submanifolds is equivalent to the Sobolev inequality for all real valued functions in C 1 c ( M ) [12].”