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Cheeger inequalities for unbounded graph Laplacians

Frank Bauer, Matthias Keller, Radosław K. Wojciechowski (2015)

Journal of the European Mathematical Society

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

Circumradius versus side lengths of triangles in linear normed spaces

Gennadiy Averkov (2007)

Colloquium Mathematicae

Given a planar convex body B centered at the origin, we denote by ℳ ²(B) the Minkowski plane (i.e., two-dimensional linear normed space) with the unit ball B. For a triangle T in ℳ ²(B) we denote by R B ( T ) the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science R B ( T ) is the optimum of the minimax location problem with distance induced by B and vertices of T as existing facilities (see, for instance, [HM03] and the references therein). Using methods...

Classical solids.

Farran, H.R., d'Azevedo Breda, A.M., Robertson, S.A. (1995)

Beiträge zur Algebra und Geometrie

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