Bounded orbits of certain diagonalizable flows on   $SL_{n}(\mathbb{R})/SL_{n}(\mathbb{Z})$
  We prove that the set of points that have bounded orbits under certain diagonalizable flows is a hyperplane absolute winning subset of $SL_{n}(\mathbb{R})/SL_{n}(\mathbb{Z})$. 
Lifan Guan and Weisheng Wu
math.DS