bio | website | pdmi.ras.ru/~svivanov |
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location | Saint Petersburg, Russia | |
age | 42 | |
visits | member for | 4 years, 11 months |
seen | Jan 6 at 19:07 | |
stats | profile views | 11,295 |
I am a research fellow at St.Petersburg Department of Steklov Math Institute
Jan 24 |
awarded | Popular Question |
Dec 3 |
awarded | Enlightened |
Dec 3 |
awarded | Nice Answer |
Dec 3 |
awarded | Nice Answer |
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 |