Lotay, JD;
Pacini, T;
(2020)
From Lagrangian to totally real geometry: coupled flows and calibrations.
Communications in Analysis and Geometry
, 28
(3)
pp. 607-675.
10.4310/CAG.2020.v28.n3.a5.
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Abstract
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-K\"ahler case, by its analogues. To this end we explore the geometry of totally real submanifolds, defining (i) a new geometric flow in terms of the ambient canonical bundle, (ii) a modified volume functional which takes into account the totally real condition. We discuss short-time existence for our flow and show it couples well with the Streets-Tian symplectic curvature flow for almost K\"ahler manifolds. We also discuss possible applications to Lagrangian submanifolds and calibrated geometry.
| Type: | Article |
|---|---|
| Title: | From Lagrangian to totally real geometry: coupled flows and calibrations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/CAG.2020.v28.n3.a5 |
| Publisher version: | https://doi.org/10.4310/CAG.2020.v28.n3.a5 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1429918 |
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