A metric deformation and the first eigenvalue of Laplacian on 1-forms
A metric deformation and the first eigenvalue of Laplacian on 1-forms
We search for a higher-dimensional analogue of Calabiās example of a metric deformation, quoted by Cheeger, which inspired him to prove an inequality between the first eigenvalue of the Laplacian on functions and an isoperimetric constant. We construct an example of a metric deformation on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper ā¦