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)

 

Convolution of convex valuations (with A. Bernig) Geometriae Dedicata 123 (2006),  153—169 (arxiv version)

 

Theory of valuations on manifolds, III. Multiplicative structure in the general case (with S. Alesker). Trans. Amer. Math. Soc. 360 (2008), 1951--1981 (arxiv version)

 

Hermitian integral geometry (with A. Bernig) Ann. of Math. 173 (2011), 907--945 (arxiv version)

 

An extension of Alexandrov's theorem on second derivatives of convex functions. Adv. Math.  228 (2011), 2258-2267 (arxiv version)

 

Integral geometry of complex space forms (with A. Bernig and G. Solanes). Geom. Funct. Anal. 24 (2014), 403--492 arXiv preprint, 2012

 

Piecewise linear approximation of smooth functions of two variables (with R.C. Scott). Adv. Math. (2013),  229--241.arXiv version, 2013

 

Ropelength criticality (with J. Cantarella, R. Kusner and J.M. Sullivan). Geometry & Topology 18 (2014), 2595--2665. (arxiv version)

 

Intersection theory and the Alesker product. To appear in Indiana U. Math. J. (arxiv version)

 

 

Lecture notes

 

 

"The two faces of Blaschkean integral geometry", Les Diablerets, Switzerland, September 2008

 

Theory and applications of the normal cycle, Rennes, France, September 2009

 

Alegbraic integral geometry, Barcelona, September 2010

 

Results and prospects in integral geometry,  Frankfurt, September 2011

 

 

Unpublished papers

 

Semidifferential topology and the ropelength problem