TY - GEN

T1 - Volume comparison via boundary distances

AU - Ivanov, Sergei

PY - 2010/12/1

Y1 - 2010/12/1

N2 - The main subject of this lecture is a connection between Gromov's filling volumes and a boundary rigidity problem of determining a Riemannian metric in a compact domain by its boundary distance function. A fruitful approach is to represent Riemannian metrics by minimal surfaces in a Banach space and to prove rigidity by studying the equality case in a filling volume inequality. I discuss recent results obtained with this approach and related problems in Finsler geometry.

AB - The main subject of this lecture is a connection between Gromov's filling volumes and a boundary rigidity problem of determining a Riemannian metric in a compact domain by its boundary distance function. A fruitful approach is to represent Riemannian metrics by minimal surfaces in a Banach space and to prove rigidity by studying the equality case in a filling volume inequality. I discuss recent results obtained with this approach and related problems in Finsler geometry.

KW - Boundary distance rigidity

KW - Filling volume

KW - Minimal filling

UR - http://www.scopus.com/inward/record.url?scp=84877834517&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84877834517

SN - 9814324302

SN - 9789814324304

T3 - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

SP - 769

EP - 784

BT - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

T2 - International Congress of Mathematicians 2010, ICM 2010

Y2 - 19 August 2010 through 27 August 2010

ER -