Mathematical Conversations

You are swimming at the center of a circular lake with a bear waiting on the shore. The bear, unable to swim, moves four times faster on land than you do in water, but once on land, you can outrun it. Can you escape?

This classic riddle has been widely discussed by math outreach platforms like Quanta and Numberphile. 

However, perfect circles are rare in nature! 

What happens when the lake isn’t circular? What if it is not two-dimensional? What if there are two bears?

We will connect these problems to (optimal) Lipschitz extensions and we will propose a number of conjectures (or riddles?).