Abstract
We construct surfaces\(T_{x_0 }^p \) with volume, first eigenvalue, andL p norm of the curvature bounded independent ofx 0, but whose Cheeger constant tends to 0 asx 0 tends to infinity.
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Robert Brooks partially supported by NSF Grant DMS-9000631 and by NSF Grant RII-8610671 and the Commonwealth of Kentucky through the Kentucky EPSCoR Program. Peter Perry partially supported by NSF Grant DMS-9006092 and by NSF Grant RII-8610671 and the Commonwealth of Kentucky through the Kentucky EPSCoR Program. Peter Petersen V partially supported by an NSF grant and an NYI award.
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Brooks, R., Perry, P. & Petersen V, P. Some examples inL p spectral geometry. J Geom Anal 3, 293–313 (1993). https://doi.org/10.1007/BF02921315
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DOI: https://doi.org/10.1007/BF02921315