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- Moscow Institute of Physics and TechnologyRU332 papers
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6 papers · 2 filters
Viterbo's conjecture for certain Hamiltonians in classical mechanics
Roman Karasev, Anastasia Sharipova
We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamilt…
More bisections by hyperplane arrangements
Pavle V. M. Blagojević, Aleksandra Dimitrijević Blagojević, Roman Karasev +1
A union of an arrangement of affine hyperplanes in is the real algebraic variety associated to the principal ideal generated by the polynomial given as the produc…
Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
Arseniy Akopyan, Roman Karasev
We study the Gromov waist in the sense of -neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gau…
On the Carathéodory number for strong convexity
Vuong Bui, Roman Karasev
We give an improvement of the Carathéodory theorem for strong convexity (ball convexity) in , reducing the Carathéodory number to in several cases; and show that t…
The Six Cylinders Problem: -symmetry Approach
Oleg Ogievetsky, Senya Shlosman
Motivated by a question of W. Kuperberg, we study the 18-dimensional manifold of configurations of 6 non-intersecting infinite cylinders of radius all touching the unit ball i…
Convex fair partitions into an arbitrary number of pieces
Arseniy Akopyan, Sergey Avvakumov, Roman Karasev
We prove that any convex body in the plane can be partitioned into convex parts of equal areas and perimeters for any integer ; this result was previously known for pri…