Minimal surfaces in the three dimensional sphere with high symmetry.

Using the Lawsonu0027s existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three dimensional sphere. These surfaces contain the Clifford torus, the Lawsonu0027s minimal surfaces, and seven new minimal surfaces with genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation between such surfaces and the maximal extendable group actions on subsurfaces of the three dimensional sphere.