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Showing 1 to 4 of 4 for “"length functions"”.
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Length functions in flat metrics
This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of Horowitz) for subfamilies of at metrics coming from q-di erentials. In addition we …
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Rigidity of length functions over strata of flat metrics
… more unmarked zeroes than the genus, the Sigma-length-spectrum of a set of simple closed curves Sigma determines the flat metric in the stratum if and only if Sigma is dense in the projective measured foliation space. We also prove that flat metrics in any stratum are locally determined by the …
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Uniform bounds in F-finite rings and their applications /
… are then used to show that the Hilbert-Kunz length functions and the normalized Frobenius splitting numbers defined on the spectrum of a ring converge uniformly to their limits, namely the Hilbert-Kunz multiplicity function and the Fsignature function. From this we establish that the …
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Asymptotic Behavior of Homology and Intersection Multiplicity
… most important one, deals with the asymptotic length of homology for complexes of finitely generated free modules, under the iteration of the Frobenius functor. We first obtain asymptotic bounds on such length functions in lower dimensional cases, which generalizes a result of Dutta. Then, we …