45 citations · 674 across the 102 of their papers we have counts for
4 papers · 2 filters
On a theorem of Grove and Searle
Oliver Knill
A theorem of Grove and Searle directly establishes that positive curvature 2d manifolds M with effective circular symmetry group of dimension 8 or less have positive Euler characte…
A Dehn type quantity for Riemannian manifolds
Oliver Knill
We look at the functional Y(M) = int_M K(x) dV(x) for compact Riemannian 2d-manifolds M, where K(x) = (2d)! (d!)^-1 (4pi)^-d int_T prod_k=1^d K_t_2k,t_2k+1(x) dt involves products…
On index expectation curvature for manifolds
Oliver Knill
Index expectation curvature K(x) = E[i_f(x)] on a compact Riemannian 2d-manifold M is the expectation of Poincare-Hopf indices i_f(x) and so satisfies the Gauss-Bonnet relation tha…
Integral geometric Hopf conjectures
Oliver Knill
The Hopf sign conjecture states that a compact Riemannian 2d-manifold M of positive curvature has Euler characteristic X(M)>0 and that in the case of negative curvature X(M) (-1)^d…