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A dual characterization of length spaces with application to Dirichlet metric spaces
"... We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. A main input is a dual characterization of length spaces in terms of the property that the 1Lipschitz functions form a sheaf. ..."
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We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. A main input is a dual characterization of length spaces in terms of the property that the 1Lipschitz functions form a sheaf.
Essential . . . EIGENFORMS, AND SPECTRA FOR THE ¯∂NEUMANN PROBLEM ON GMANIFOLDS.
, 2011
"... Let M be a complex manifold with boundary, satisfying a subelliptic estimate, which is also the total space of a principal G–bundle with G a Lie group and compact orbit space M — /G. Here we investigate the ¯ ∂Neumann Laplacian □ on M. We show that it is essentially selfadjoint on its restrictio ..."
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Let M be a complex manifold with boundary, satisfying a subelliptic estimate, which is also the total space of a principal G–bundle with G a Lie group and compact orbit space M — /G. Here we investigate the ¯ ∂Neumann Laplacian □ on M. We show that it is essentially selfadjoint on its restriction to compactly supported smooth forms. Moreover we relate its spectrum to the existence of generalized eigenforms: an energy belongs to σ(□) if there is a subexponentially bounded generalized eigenform for this energy. Vice versa, there is an expansion in terms of these well–behaved eigenforms so that, spectrally, almost every energy comes with such a generalized eigenform.