Local Hausdorff dimension and measure

Series: 
SIAM Student Seminar
Friday, February 12, 2016 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 114
,  
Georgia Institute of Technology
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local measure. We show that in many circumstances we can recover the global Hausdorff dimension from the local one. We give an example of a compact metric space with a continuum of local dimension values. We define the dimension of a measure and connect the definition to that of local Hausdorff dimension and measure for a class of spaces called (variable) Ahlfors Q-regular.  Very little background knowledge, aside from basic familiarity with metric spaces, will be assumed.