Related papers: A sharp lower bound on the polygonal isoperimetric…
Without assuming the Northcott property we provide an upper bound on the number of "big solutions" of a special system of Diophantine inequalities over proper adelic curves. This system is interesting since it is a stronger version Roth's…
In the paper, some lower bounds for polygamma functions are refined.
A sharp Poincar\'e-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso second-variation inequality. The…
In this paper, we investigate the reverse improvement property of Sobolev inequalities on manifolds with quadratically decaying Ricci curvature. Specifically, we establish conditions under which the uniform decay of the heat kernel implies…
Sharp lower and upper uniform estimates are obtained for fundamental frequencies of $p$-Laplace type operators generated by quadratic forms. Optimal constants are exhibited, rigidity of the upper estimate is proved, anisotropic…
We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
We obtain some new inequalities of Chebyshev Type.
In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.
The `full' edge isoperimetric inequality for the discrete cube (due to Harper, Bernstein, Lindsay and Hart) specifies the minimum size of the edge boundary $\partial A$ of a set $A \subset \{0,1\}^n$, as a function of $|A|$. A weaker (but…
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has {\em unit determinant}. Our result…
In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompact Riemannian manifolds with asymptotically nonnegative curvature using standard comparison methods in Riemannian Geometry. These methods…
We present functional-type a posteriori error estimates in isogeometric analysis. These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the exact error in the energy norm. {Moreover, since these…
We prove a sharp dimension-free isoperimetric inequality, involving the volume entropy, in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are…
We give a uniform estimate and an inequality for solutions of an equation with Dirichlet boundary condition.
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this…