4 citations · 12 across the 10 of their papers we have counts for
11 papers
Central figure-8 cross-cuts make surfaces cylindrical
Bruce Solomon
We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and al…
Constant mean curvature, flux conservation, and symmetry
Nick Edelen, Bruce Solomon
As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Th…
Surfaces with central cross-sections
Bruce Solomon
A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse ova…
X-rays of currents and projections of forms
Bruce Solomon
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our…
Central cross-sections make surfaces of revolution quadric
Bruce Solomon
We prove here that when all planes transverse and nearly perpendicular to the axis of a surface of revolution intersect it in loops having central symmetry, the surface must be qua…
Skew loops in flat tori
Bruce Solomon
We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More su…