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The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera, Andrew Swann (2008)

Annales de l’institut Fourier

We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kähler forms. This gives a practical method to compute the intrinsic torsion and is applied in a number of examples. In addition we find simple characterisations of HKT and QKT geometries entirely in the exterior algebra and compute how the intrinsic torsion...

The inverse mean curvature flow and p -harmonic functions

Roger Moser (2007)

Journal of the European Mathematical Society

We consider the level set formulation of the inverse mean curvature flow. We establish a connection to the problem of p -harmonic functions and give a new proof for the existence of weak solutions.

The Kähler Ricci flow on Fano manifolds (I)

Xiuxiong Chen, Bing Wang (2012)

Journal of the European Mathematical Society

We study the evolution of pluri-anticanonical line bundles K M - ν along the Kähler Ricci flow on a Fano manifold M . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of M . For example, the Kähler Ricci flow on M converges when M is a Fano surface satisfying c 1 2 ( M ) = 1 or c 1 2 ( M ) = 3 . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....

The Kuranishi space of complex parallelisable nilmanifolds

Sönke Rollenske (2011)

Journal of the European Mathematical Society

We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.

The Laplace-Beltrami operator in almost-Riemannian Geometry

Ugo Boscain, Camille Laurent (2013)

Annales de l’institut Fourier

We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...

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