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14 papers · 1 filter
Dirac operators on cobordisms: degenerations and surgery
Daniel F. Cibotaru, Liviu I. Nicolaescu
We investigate the Dolbeault operator on a pair of pants, i.e., an elementary cobordism between a circle and the disjoint union of two circles. This operator induces a canonical se…
Developments around positive sectional curvature
Karsten Grove
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. I…
On Certain Vanishing Identities For Gromov-Witten Invariants
Xiaobo Liu
In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range…
Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
Boris Khesin, Jonatan Lenells, Gerard Misiolek
We study an equation lying `mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magne…
Lifting Group Actions and Nonnegative Curvature
Karsten Grove, Wolfgang Ziller
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric o…
Structure theorems for embedded disks with mean curvature bounded in L^P
Giuseppe Tinaglia
After appropriate normalizations an embedded disk whose second fundamental form has large norm contains a multi-valued graph, provided the L^P norm of the mean curvature is suffici…