ISSN:0010-3640    

DOI:10.1002/cpa.3160460702

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460703

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe classical surgery theory (see [5] and [23]) computes the structure setSm(M, rel ∂) of manifolds homotopy equivalent toMrelative to the boundary. Siebenmann showed that in topological category, the structure set is 4‐periodic:Sm(M, rel ∂) ≅Sm+4(M×D4, rel ∂) up to a copy of ℤ; see [12]. Cappell and Weinberger gave a geometric interpretation of this periodicity in [8]. By using Weinberger's stratified surgery theory (see [24]), we extend this to an equivariant periodicity result for topological manifolds with homotopically stratified actions by compact Lie groups, withD4replaced by the unit ball of certain group representations. In particular, ifGis an odd order group acting on a topological manifoldM, then the equivariant stable structure sets satisfyS G−∞(M, rel ∂) ≅S G−∞(M×D(ℝ4⊗ ℝG), rel ∂) up to cop

ISSN:0010-3640    

DOI:10.1002/cpa.3160460704

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractWave maps are critical pointsU:M→Nof the Lagrangian ℒ︁[U] = ∞M‖dU‖2, whereMis an Einsteinian manifold andNa Riemannian one. For the caseM= ℝ2,1andUa spherically symmetric map, it is shown that the solution to the Cauchy problem forUwith smooth initial data of arbitrary size is smooth for all time, provided the target manifoldNsatisfies the two conditions that: (1) it is either compactorthere exists an orthonormal frame of smooth vectorfields onNwhose structure functions are bounded; and (2) there are two constantscandCsuch that the smallest eigenvalue λ and the largest eigenvalue λ of the second fundamental formkABof any geodesic sphere Σ(p, s) of radiusscentered atpϵNsatisfysλ ≧candsA ≦C(1 +s).This is proved by first analyzing the energy‐momentum tensor and using the second condition to show that near the first possible singularity, theenergyof the solution cannot concentrate, and hence is small. One then proves that for targets satisfying the first condition, initial data of small energy imply global regularity of the solution. ©

ISSN:0010-3640    

DOI:10.1002/cpa.3160460705

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460701

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY