Results 11 to 20 of about 196 (81)

Functional inequalities for the heat flow on time‐dependent metric measure spaces

Journal of the London Mathematical Society, Volume 104, Issue 2, Page 926-955, September 2021., 2021
Abstract We prove that synthetic lower Ricci bounds for metric measure spaces — both in the sense of Bakry–Émery and in the sense of Lott–Sturm–Villani — can be characterized by various functional inequalities including local Poincaré inequalities, local logarithmic Sobolev inequalities, dimension independent Harnack inequality, and logarithmic Harnack 
Eva Kopfer, Karl‐Theodor Sturm
wiley   +1 more source

Optimal L^p Hardy-Rellich type inequalities on the sphere

, 2020
In this paper we study some Lp -Hardy-Rellich type inequalities and the corresponding optimal constant on the geodesic sphere. By the divergence theorem, properties of radial Laplacian and geodesic distance, we obtain an improved version of Hardy-Rellich
Abimbola Ayodeji Abolarinwa, K. Rauf
semanticscholar   +1 more source

A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbation

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
We generalize the Zermelo navigation on Riemannian manifolds (M; h), admitting a space dependence of a ship's speed 0 < |u(x)|h ≤ 1 in the presence of a perturbation W̃ determined by a strong (critical) velocity vector field satisfying |W̃ (x)|h = |u(x ...
Kopacz Piotr
doaj   +1 more source

Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products

Analysis and Geometry in Metric Spaces, 2022
Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞.
Casteras Jean-Baptiste, Heinonen Esko, Holopainen Ilkka, De Lira Jorge H.   +3 more
doaj   +1 more source

The β-Flatness Condition in CR Spheres

Advanced Nonlinear Studies, 2017
This work is an adaptation of one of the methods based on the variational critical points at infinity theory of Abbas Bahri [1, 3, 2, 4, 5, 6, 7, 8] to the Cauchy–Riemann settings.
Gamara Najoua, Hafassa Boutheina
doaj   +1 more source

On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow

Analysis and Geometry in Metric Spaces, 2023
The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space (M,g,e−ϕdVg,m)\left(M,g,{e}^{-\phi }{\rm{d}}{V}_{g},m), the ...
Ho Pak Tung, Shin Jinwoo
doaj   +1 more source

Limits of Riemannian 4‐manifolds and the symplectic geometry of their twistor spaces

Transactions of the London Mathematical Society, Volume 4, Issue 1, Page 100-109, December 2017., 2017
Abstract The twistor space of a Riemannian 4‐manifold carries two almost complex structures, J+ and J−, and a natural closed 2‐form ω. This article studies limits of manifolds for which ω tames either J+ or J−. This amounts to a curvature inequality involving self‐dual Weyl curvature and Ricci curvature, and which is satisfied, for example, by all anti‐
Joel Fine
wiley   +1 more source

Singular limits solution for 2-dimensional elliptic problems involving exponential nonlinearities with sub-quadratic convection nonlinear gradient terms and singular weights

Advances in Nonlinear Analysis, 2014
Given a bounded open regular set Ω of ℝ2$\mathbb {R}^2$, q1,...,qK∈Ω${q_1, \ldots , q_K \hspace*{-0.85358pt}\in \hspace*{-0.85358pt} \Omega }$, a regular bounded function ϱ:Ω→[0,+∞)${\varrho \hspace*{-0.56905pt}:\hspace*{-0.56905pt} \Omega \hspace*{-0 ...
Baraket Sami, Ouni Taieb
doaj   +1 more source

On the topology of closed manifolds with quasi-constant sectional curvature

Journal de l'École polytechnique. Mathématiques, 2019
We prove that closed manifolds admitting a metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC space where sets of isotropic points are arbitrary, under suitable positivity assumption ...
L. Funar
semanticscholar   +1 more source

Smooth long‐time existence of Harmonic Ricci Flow on surfaces

Journal of the London Mathematical Society, Volume 95, Issue 1, Page 277-304, February 2017., 2017
Abstract We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long‐time existence for the Harmonic Ricci Flow with large coupling constant.
Reto Buzano, Melanie Rupflin
wiley   +1 more source