Lower Bounds For 2-systoles
Similarly, just about the only nontrivial lower bound for a k-systole with k = 2, results from recent work in gauge theory and J-holomorphic curves. The study of lower bounds for the conformal 2-systole of 4-manifolds has led to a simplified proof of the density of the image of the period map, by Jake Solomon.
Read more about this topic: Systolic Geometry
Famous quotes containing the word bounds:
“What comes over a man, is it soul or mind
That to no limits and bounds he can stay confined?
You would say his ambition was to extend the reach
Clear to the Arctic of every living kind.
Why is his nature forever so hard to teach
That though there is no fixed line between wrong and right,
There are roughly zones whose laws must be obeyed?”
—Robert Frost (18741963)