相关论文: Rigidity in the Planar Ulam Floating Body Problem …
We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer this problem in the class of origin symmetric n-dimensional…
We give a negative answer to Ulam's Problem 19 from the Scottish Book asking {\it is a solid of uniform density which will float in water in every position a sphere?} Assuming that the density of water is $1$, we show that there exists a…
We study a new construction of bodies from a given convex body in $\mathbb{R}^{n}$ which are isomorphic to (weighted) floating bodies. We establish several properties of this new construction, including its relation to $p$-affine surface…
This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in a liquid in any orientation. Despite recent results of F. Wegner pointing towards an affirmative answer, a…
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
We present a simple experimental realization of a two-dimensional floating body that can remain in equilibrium in any orientation. This system is based on a class of shapes known as Zindler curves, which possess the remarkable geometric…
We consider rigidity properties of steady Euler flows in two-dimensional bounded domains. We prove that steady Euler flows in a disk with exactly one interior stagnation point and tangential boundary conditions must be circular flows, which…
We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This…
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive…
We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the…
In this paper, we study the uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the compressible…
We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…
We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential…
In this paper, we prove a rigidity theorem for smooth strictly convex domains in Euclidean spaces.
This paper determines the optimal upper bound for the simultaneous packing and covering constants of the two-dimensional centrally symmetric convex domains. It solved a problem opening for more than thirty years.
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
We show that any sufficiently (finitely) smooth $\mathbb Z_2$-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid, i.e. all deformations among domains in the same class which preserve the length…
We find a reentrant columnar-to-squamous rigidity transition in 3D epithelia, governed by volume- and area elasticity. Our framework maps onto the classic 2D Area- and Perimeter-Elasticity model but, unlike its 2D counterpart, exhibits both…
The article contains the results of the author's recent investigations of rigidity problems of domains in Euclidean spaces carried out for developing a new approach to the classical problem of the unique determination of bounded closed…
We prove that a convex polytope $P \subset \mathbb{R}^d$, $d \ge 2$, of uniform density $\delta \in (0,1)$ floating in a liquid of density $1$, is uniquely determined by its surface of flotation $P_{[\delta]}$ whenever $\delta \neq…