On a family of Lagrangian submanifolds in bidisks and Lagrangian Hofer metric

TL;DR

This paper constructs a vast family of Lagrangian submanifolds in bidisks with unbounded Lagrangian Hofer diameters and establishes an inequality for the Lagrangian Hofer metric similar to known results for complex balls.

Contribution

It introduces a new family of Lagrangian submanifolds with unbounded Hofer diameters and proves a related inequality for the Hofer metric.

Findings

Uncountably many Lagrangian submanifolds with unbounded Hofer diameter

A new inequality for the Lagrangian Hofer metric

Extension of known inequalities to bidisk setting

Abstract

We construct a family of uncountably many Lagrangian submanifolds in the standard bidisks such that the Lagrangian Hofer diameter associated to each Lagrangian submanifold is unbounded. We also prove a certain inequality of the Lagrangian Hofer metric which is of the same type as S. Seyfaddini's for the case of the real form of the complex $n$-ball.