0000000000679118
AUTHOR
De-jun Feng
Local conical dimensions for measures
AbstractWe study the decay of μ(B(x,r)∩C)/μ(B(x,r)) asr↓ 0 for different kinds of measures μ on ℝnand various conesCaroundx. As an application, we provide sufficient conditions that imply that the local dimensions can be calculated via cones almost everywhere.
Self-affine sets in analytic curves and algebraic surfaces
We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces do not contain non-trivial self-affine sets. peerReviewed