Recent papers

Stucture of the unitary valuation algebra, ,Journal of Differential Geom. 72 (2006) , (arxiv version)

Criticality for the Gehring link problem (joint with J. Cantarella, R. Kusner, J. Sullivan and N. Wrinkle)  Geometry & Topology 10 (2006) 2045-2015 (arxiv version)

Circles minimize most knot energies (joint with A. Abrams, J. Cantarella, M. Ghomi and R. Howard) Topology 42 (2003), Pages 381-394 (arxiv version)

 

Convolution of convex valuations (with A. Bernig) Geometriae Dedicata (2006?), (arxiv version)

 

Theory of valuations on manifolds, III. Multiplicative structure in the general case (with S. Alesker). Trans. Amer. Math. Soc. (arxiv version)

 

Hermitian integral geometry (with A. Bernig) (arxiv version)

 

An extension of Alexandrov's theorem on second derivatives of convex functions (arxiv version)

 

 

Lecture notes

 

 

Here are the slides from my recent lecture series "The two faces of Blaschkean integral geometry"

 

 

 

Unpublished papers

 

Semidifferential topology and the ropelength problem