bio | website | pdmi.ras.ru/~svivanov |
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location | Saint Petersburg, Russia | |
age | 42 | |
visits | member for | 4 years, 7 months |
seen | 2 days ago | |
stats | profile views | 11,042 |
I am a research fellow at St.Petersburg Department of Steklov Math Institute
Sep 17 |
awarded | Enlightened |
Sep 17 |
awarded | Nice Answer |
Sep 6 |
awarded | Enlightened |
Sep 6 |
awarded | Nice Answer |
Jul 2 |
awarded | Curious |
Apr 28 |
awarded | Good Answer |
Mar 29 |
awarded | Popular Question |
Mar 3 |
awarded | Yearling |
Feb 24 |
awarded | gn.general-topology |
Feb 24 |
awarded | Enlightened |
Feb 23 |
awarded | Nice Answer |
Feb 23 |
answered | Is a left topological group which is a manifold a topological group? |
Feb 17 |
comment |
Characterization of discs
There are still counter-examples with the formulation "open set homeomorphic to the disc". For example, start with the unit disc and remove a segment between a point in the boundary and a point inside. You can then remove a small disc centered at the interior endpoint, and so on. In these examples, the boundary contains the unit circle so the property holds as stated. You need to assume that there are no other points on $L\cap\partial D$. |
Feb 17 |
comment |
A Converse to the Gauss Bonnet Theorem
For example, contract a hemisphere to a segment by contracting each radial circle to a point. The resulting space is a bouquet of a sphere and a circle. Place the segment to the sphere by an injective map. This can be made smooth. |
Feb 14 |
comment |
A Converse to the Gauss Bonnet Theorem
Take a point with the highest $z$-coordinate. If it is on the boundary, take one with the lowest $z$-coordinate. Since the entire boundary is on the same level, either a highest or lowest point is in the interior. |
Feb 12 |
answered | A Converse to the Gauss Bonnet Theorem |
Jan 2 |
awarded | Nice Question |
Dec 14 |
comment |
Example of non-closed convex hull in a CAT(0) space
Thanks, now I understand. Indeed the Euclidean intuition fails. |
Dec 13 |
comment |
Example of non-closed convex hull in a CAT(0) space
@Anton, I don't get it. In any manifold, take a point $p$ and a nearby small ball $B$, and connect $p$ to all points of $B$ by geodesic segments. I believe the resulting set is convex if everything is small enough, yet the conical part of the boundary is filled by geodesics. |
Dec 9 |
comment |
Tverberg's theorem in CAT(0) spaces
Answering my previous comment: see Theorem 1.1 in arXiv:1011.1802 for $r=2$. (Thanks to Roman Karasev who informed me about this reference.) |