New Yamabe-type flow in a compact Riemannian manifold

被引：0

作者：

Ma, Li ^{[1
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Xueyuan Rd 30, Beijing 100083, Peoples R China

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2023年 / 184卷

基金：

中国国家自然科学基金;

关键词：

Yamabe-type flow; Global existence; Norm-preserving flow; Scalar curvature; Asymptotic behavior; PRESCRIBING GAUSSIAN CURVATURE; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; CONVERGENCE;

D O I：

10.1016/j.bulsci.2023.103244

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we set up a new Yamabe type flow on a compact Riemannian manifold (M, g) of dimension n & GE; 3. Let & psi;(x) be any smooth function on M. Let p = n+2 n-2 and cn = 4(n-1) n-2 . We study the Yamabe-type flow u = u(t) satisfyingut = u1-p(cn & UDelta;u -& psi;(x)u) + r(t)u, in M x (0 , T) , T > 0withr(t) = M (cn| backward difference u|2 + & psi;(x)u2)dv/ M up+1 ,which preserves the Lp+1(M )-norm and we can show that for any initial metric u0 > 0, the flow exists globally. We also show that in some cases, the global solution converges to a smooth solution to the equationcn & UDelta;u - & psi;(x)u + r(& INFIN;)up = 0 , on M

引用

页数：19