TY - JOUR
T1 - Smooth submanifolds intersecting any analytic curve in a discrete set
AU - Coman, Dan
AU - Levenberg, Norman
AU - Poletsky, Evgeny A.
PY - 2005/5
Y1 - 2005/5
N2 - We construct examples of C ∞ smooth submanifolds in ℂn and ℝn of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real n-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar.
AB - We construct examples of C ∞ smooth submanifolds in ℂn and ℝn of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real n-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar.
UR - http://www.scopus.com/inward/record.url?scp=17444429600&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=17444429600&partnerID=8YFLogxK
U2 - 10.1007/s00208-004-0616-0
DO - 10.1007/s00208-004-0616-0
M3 - Article
AN - SCOPUS:17444429600
SN - 0025-5831
VL - 332
SP - 55
EP - 65
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1
ER -