Isoperimetric inequalities for the heat potential operator

Carleman Inequalities and the Heat Operator

1. Introduction. The unique continuation property is best understood for second-order elliptic operators. The classic paper by Carleman [8] established the strong unique continuation theorem for second-order elliptic operators that need not have analytic coefficients. The powerful technique he used, the so-called " Carleman weighted inequality, " has played a central role in later developments....

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07

Isoperimetric inequalities for soluble groups

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.

Isoperimetric inequalities for Random Walks

Isoperimetric inequalities for minimal graphs

Based on Markvorsen and Palmer work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N × R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. Mathematics Subject Classification: (2000): Primary 53C42; Secondary 53A10