Results 31 to 40 of about 534 (49)

On common zeros of eigenfunctions of the Laplace operator

, 2016
We consider the eigenfunctions of the Laplace operator $\Delta $ on a compact Riemannian manifold of dimension $n$. For $M$ homogeneous with irreducible isotropy representation and for a fixed eigenvalue of $\Delta $ we find the average number of common ...
Akhiezer, Dmitri, Kazarnovskii, Boris
core   +1 more source

Blowing-up solutions concentrated along minimal submanifolds for some supercritical Hamiltonian systems on Riemannian manifolds

Advances in Nonlinear Analysis
Let (ℳ,g)\left({\mathcal{ {\mathcal M} }},g) and (K,κ)\left({\mathcal{K}},\kappa ) be two Riemannian manifolds of dimensions NN and mm, respectively. Let ω∈C2(ℳ)\omega \in {C}^{2}\left({\mathcal{ {\mathcal M} }}) satisfy ω>0\omega \gt 0.
Chen Wenjing, Wang Zexi
doaj   +1 more source

Comparison formulas for total mean curvatures of Riemannian hypersurfaces

Advanced Nonlinear Studies
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds.
Ghomi Mohammad
doaj   +1 more source

On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture [PDF]

, 2012
We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$ is the area radius of $S$
Khuri, Marcus A, Weinstein, Gilbert, Yamada, Sumio   +2 more
core  

A note on twisted Dirac operators on closed surfaces

, 2018
We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\rm Spin^c$ Dirac operator.
Branding, Volker
core   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

Stability and critical dimension for Kirchhoff systems in closed manifolds

Advanced Nonlinear Studies
The Kirchhoff equation was proposed in 1883 by Kirchhoff [Vorlesungen über Mechanik, Leipzig, Teubner, 1883] as an extension of the classical D’Alembert’s wave equation for the vibration of elastic strings. Almost one century later, Jacques Louis Lions [“
Hebey Emmanuel
doaj   +1 more source

Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces. [PDF]

Calcolo, 2021
Bachini E, Manzini G, Putti M.
europepmc   +1 more source

THE BEST-CONSTANT PROBLEM FOR A FAMILY OF GAGLIARDO–NIRENBERG INEQUALITIES ON A COMPACT RIEMANNIAN MANIFOLD

Proceedings of the Edinburgh Mathematical Society, 2003
Christophe Brouttelande
semanticscholar   +1 more source

Exponential coordinates and regularity of groupoid heat kernels

Open Mathematics, 2014
So Bing
doaj   +1 more source