Related papers: Remarks on rigidity properties of conics
This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…
In this note, we present two arguments showing that the classical \textit{linear adjoint cone restriction conjecture} holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The…
We present certain Liouville properties of eigenfunctions of second-order elliptic operators with real coefficients, via an approach that is based on stochastic representations of positive solutions, and criticality theory of second-order…
In this work, optimal rigidity results for eigenvalues on K\"ahler manifolds with positive Ricci lower bound are established. More precisely, for those K\"ahler manifolds whose first eigenvalue agrees with the Ricci lower bound, we show…
In this paper I will explain a rigidity conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. I will also establish a simple case of the conjecture, the one involving the $3$-diagonal map on a convex $8$-gon…
We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of the two maps while preserving the orders of their…
For smooth surfaces properly immersed in the unit ball of $\RR^n$ with density close to one and small Willmore energy, the optimal a priori estimate(bi-Lipschitz and $W^{2,2}$ parametrization)is provided. We also discuss the quantitative…
We show that all PL manifolds of dimension $\geq 3$ have spines similar to Bing's house with two rooms. Beyond this we explore approximation rigidity and an $h$-principle.
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…
Symplectic billiards were introduced by Albers and Tabachnikov as billiards in strictly convex bounded domains of the plane with smooth boundary having a specific law of reflection. This paper proves a rigidity result for symplectic…
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…
We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the $w^*$-LD$2$P, the $w^*$-D$2$P, the LD$2$P, and the SD$2$P in…
In this article, we consider linearly convex complex cones in complex Banach spaces and we define a new projective metric on these cones. Compared to the hyperbolic gauge of Rugh, it has the advantage of being explicit, and easier to…
In this work, we study compact Riemannian manifolds with boundary satisfying V-static-type equations. By combining a generalized Reilly formula with Steklov-type boundary value problems, we derive integral inequalities for geometric…
We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…
Homology of the circle with non-trivial local coefficients is trivial. From this well-known fact we deduce geometric corollaries concerning links of codimension two. In particular, the Murasugi-Tristram signatures are extended to invariants…
One of the most interesting problems in the theory of Birkhoff billiards is the problem of integrability. In all known examples of integrable billiards, the billiard tables are either conics, quadrics (closed ellipsoids as well as unclosed…
This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\ni\gamma$-torsional rigidity $\mathcal{T}_{\gamma,\mathsf{g}}$ on a complete Riemannian…
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the…
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd…