Polar sets of fractional Brownian sheets

The properties of the polar sets are discussed for a real-valued (N, d)-fractional Brownian sheet with Hurst index. Sufficient conditions and necessary conditions for a compact set to be polar for the fractional Brownian sheet are proved. The infimum of Hausdorff dimensions of its polar sets are also obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity. Research supported by the National Natural Foundation of China (10471148), the Sci-tech Innovation Item for Excellent Young and Middle-Aged University Teachers of Educational Department of Hubei (200316).