English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In [LW], we construct examples of two-dimensional Hamiltonian stationaryself-shrinkers and self-expanders for Lagrangian mean curvature flows, whichare asymptotic to the union of two Schoen-Wolfson cones. These self-shrinkersand self-expanders can be glued together to yield solutions of the Brakke flow- a weak formulation of the mean curvature flow. Moreover, there is no massloss along the Brakke flow. In this paper, we generalize these results tohigher dimension. We construct new higher dimensional Hamiltonian stationarycones of different topology as generalizations of the Schoen-Wolfson cones.Hamiltonian stationary self-shrinkers and self-expanders that are asymptotic tothese Hamiltonian stationary cones are also constructed. They can also be gluedtogether to produce eternal solutions of the Brakke flow without mass loss.Finally, we show the same conclusion holds for those Lagrangian self-similarexamples recently found by Joyce, Tsui and the first author in [JLT].

Hamiltonian stationary cones and self-similar solutions in higher dimension