Related papers: Gradient flows of $(K,N)$-convex functions with ne…
In this manuscript, we extend the global gradient estimates for positive solutions to the heat equation under a general compact Finsler $CD(-K,N)$ geometric flow and derive the corresponding Harnack inequality.
We introduce and study a multivariate function that counts nowhere-zero flows on a graph G, in which each edge of G has an individual capacity. We prove that the associated counting function is a piecewise-defined polynomial in these…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
In this paper, we study the convexity, interior gradient estimate, Liouville type theorem and asymptotic behavior at infinity of translating solutions to mean curvature flow as well as the nonlinear flow by powers of the mean curvature.
We analyze a gradient flow of closed planar curves minimizing the anisoperimetric ratio. For such a flow the normal velocity is a function of the anisotropic curvature and it also depends on the total interfacial energy and enclosed area of…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
If $u : \Omega\subset \mathbb{R}^d \to {\rm X}$ is a harmonic map valued in a metric space ${\rm X}$ and ${\sf E} : {\rm X} \to \mathbb{R}$ is a convex function, in the sense that it generates an ${\rm EVI}_0$-gradient flow, we prove that…
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of…
In this work, we introduce the class of $h$-${\rm{MN}}$-convex functions by generalizing the concept of ${\rm{MN}}$-convexity and combining it with $h$-convexity. Namely, Let $I,J$ be two intervals subset of $\left(0,\infty\right)$ such…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…
In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
In this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci flow.…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the universe by different geometries. Field transformations for functional flow equations…
On a complete Riemannian manifold $M$, we study the spectral flow of a family of Callias operators. We derive a codimension zero formula when the dimension of $M$ is odd and a codimension one formula when the dimension of $M$ is even. These…