2024 Kazdan-warner type equation

Kazdan-warner type equation

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August undefined, 2024

WebbThe current article is to study the solvability of Nirenberg problem on S 2 through the so-called Gaussian curvature flow. We aim to propose a unified method to treat the problem for candidate functions without sign restriction and non-degenerate assumption. As a first step, we reproduce the following statement: suppose the critical points of a smooth … Webb19 juni 2024 · We finally provide some applications of our main results by dealing with some Yamabe-type and Kazdan-Warner-type equations on locally finite weighted graphs. Submission history From: Giorgio Stefani [ view email ] [v1] Sat, 19 Jun 2024 07:57:08 UTC (14 KB) Download: PDF PostScript Other formats ( license) Current …

Kazdan-Warner Problem on Compact Riemann Surfaces with

WebbSemi-linear equations on graphs, variational method, Yamabe-type equation, Kazdan–Warner-type equation, Brezis–Strauss Theorem. Acknowledgements. The authors are members of INdAM–GNAMPA. The ﬁrst author is partially supported by the INdAM–GNAMPA Project 2024 Convergenze variazionali per funzionali e operatori … Webb24 jan. 2024 · We consider the following Kazdan–Warner equation \begin {aligned} -\Delta _ {g}u=8\pi \left ( \dfrac {he^ {u}} {\int _ {\Sigma }he^ {u}\mathop {}\mathrm {d}\mu _ {g}}-1\right) . \end {aligned} (1.1) Here \Delta _ {g} is the Laplace–Beltrami operator. The solutions to ( 1.1) are the critical points of the following functional: clockwise what direction

arXiv:math/0306132v1 [math.AP] 7 Jun 2003

Webb19 juni 2024 · When $m=1$, we also establish a uniqueness result in the spirit of the Brezis-Strauss Theorem. We finally provide some applications of our main results by dealing with some Yamabe-type and... Webb15 sep. 2024 · In this short paper, we reinvestigate the Kazdan–Warner equation Δ u = c − h e u with c < 0 on G, where h defined on V is a known function. Grigor'yan, Lin and Yang showed that if the Kazdan–Warner equation has a … Webb3 juni 2008 · In this paper, we discuss a Kazdan-Warner typed equation on certain non-compact Riemannian manifolds. As an application, we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact Kähler manifolds. Download to read the full article text. clockwise webmd

Existence of Conformal Metrics with Prescribed Q-Curvature

Kazdan-Warner equation on graph in the negative case

WebbKAZDAN-WARNER PROBLEM ON COMPACT RIEMANN SURFACES WITH SMOOTH BOUNDARY JIE XU ... and M. Rigoli. Yamabe type equations with a sign-changing nonlinearity, and the pre-scribed curvature problem. Journal of Diﬀerential Equations, 260(10):7416–7497, 2016. [4] J. Bourguignon and J. Ezin. Scalar curvature functions in … Webb1 okt. 2024 · In the beginning, the Kazdan–Warner equation, Δ g u = c − h e u (refer to [2], [3], [13], [14], [15], [16] ), describes a conformal deformation on the smooth metric g on a 2-dimensional closed Riemannian manifold ( M, g), with both c and h are independent of the geometry of ( M, g), where c is a constant and h is some stipulated function. bodewo loginWebb10 apr. 2024 · This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be ... clockwise什么意思

"Webb20 feb. 2024 · The Kazdan–Warner equation was generalized by Ge and Jiang to certain infinite graphs. Recently, many results also have been obtained for parabolic equations on graphs. The blow-up phenomenon of the semilinear heat equation was studied by Lin and Wu [13, 21] on locally finite graphs. Lin and Yang proposed a heat flow for the mean … " - Kazdan-warner type equation

Kazdan-warner type equation

Curvature Functions for Compact 2-Manifolds (1974) Jerry L. Kazdan …

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WebbWith the help of these results, we finally give various conditions such that the p th Kazdan–Warner equation Δ p u = c − h e u has a solution on V for given h ∈ C (V) and c ∈ ℝ. Thus we generalize Grigor’yan, Lin and Yang’s work Kazdan–Warner equation on graph, Calc. Var. Partial Differential Equations 55 (4) (2016) Paper No ... Webb23 dec. 2024 · In this paper, we study the following Kazdan-Warner equation with sign-changing prescribed function h −∆u = 8π View PDF on arXiv Save to Library Create Alert Cite 4 Citations Citation Type More Filters Another remark on a result of Ding-Jost-Li …

Webb16 mars 2024 · The Kazdan–Warner equation arises from the basic geometric question which functions are potential Gaussian curvatures of 2-dimensional manifolds. Kazdan and Warner studied this question on compact manifolds [ 29] and on open manifolds that are diffeomorphic to an open set in a compact manifold [ 30 ]. Webb18 sep. 2024 · Abstract: We investigate the Kazdan-Warner equation on a network. In this case, the differential equation is defined on each edge, while appropriate transition conditions of Kirchhoff type are prescribed at the vertices. We show that the Kazdan-Warner theory extends to the present setting and we study also the critical case.

Webb1 apr. 2006 · Une identité de type Kazdan–Warner pour la. σ. k. -courbure. We prove a Kazdan–Warner type identity involving the σ k curvature and a conformal Killing vector field on a compact manifold. Our method also works to provide a unified proof for the necessary conditions in the Christoffel–Minkowski problem. http://math.tju.edu.cn/info/1622/7331.htm

Webb12 mars 2024 · A class of semilinear equations with the exponential nonlinearity, so-called Kazdan-Warner equations and the Liouville equations, also have been studied in these papers [15,18, 19,...

Webb30 sep. 2011 · In this paper, we establish existence results for positive solutions to the Lichnerowicz equations of the following type in closed manifolds -\Delta u = A (x)u^ {-p} - B (x)u^ {q},\quad { {\rm in}}\, M, where p > 1, q > 0, and A ( x ) > 0, B ( x ) ≥ 0 are given smooth functions. clockwise waterWebbIn order to apply the method of moving planes to equation (*), it requires the function R be monotone decreasing. However, we want our R to satisfy conditions of Kazdan-Warner type; hence it must not be monotone in the whole domain. To circumvent this difficulty, we introduce a new unknown function v(x) = u(x) - \x\2. bodewes mobilityWebb31 jan. 2024 · Remark 4.1 Using the reduced, static Keller–Segel equation also, equations similar to the Kazdan–Warner equation were studied in [Reference Bonheure, Casteras and Noris 3, Reference Wang, Wang and Yang 9]. These equations however are still on the plane so the geometric interpretation above is lost. bode wilde hockey bodewes sportschoolWebb10 apr. 2024 · Jie Xu. In this article, we show that (i) any smooth function on compact Riemann surface with non-empty smooth boundary can be realized as a Gaussian curvature function; (ii) any smooth function on can be realized as a geodesic curvature function for some metric . The essential steps are the existence results of Brezis-Merle … clockwise yorkshire house greek streetWebb2 aug. 2024 · The proof relies on a priori estimates for functions satisfying generalised Kazdan–Warner equations. We relate our results to the work of Hong, Jost, and Struwe on classical vortices, and that of Haydys and Walpuski on the Seiberg–Witten equations with multiple spinors. bodewhin cauthonWebb10 jan. 2024 · M. Keller and M. Schwarz, “The Kazdan-Warner equation on canonically compactifiable graphs,” Calculus of Variations and Partial Differential Equations, vol. 57, no. 2, p. 70, 2024. View at:Publisher Site Google Scholar N. Zhang and L. Zhao, “Convergence of ground state solutions for nonlinear Schrödinger equations on … bode wilde elite prospects