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dawo
Posts:
1
Registered:
11/24/10


Intersection of ball with hyperplane
Posted:
Nov 24, 2010 5:48 AM


Hello Everyone!
I have the following problem: Consider the scalled unit sphere w.r.t. the pnorm, i.e. tB with
B = {x in R^n: x_p = 1}, t>0 and p>1
and the hyperplane
H = {x in R^n: sum x_i = 1}.
I am interested in the intersection of H and tB (of course only in the cases where it is not empty). My conjecture is that all the points in the intersection have the same distance to (1/n, ..., 1/n) (in the pnorm).
My questions: (1) Is this correct? (2) If yes, what is the distance?
I would be very thankful for either a solution or a hint where to look this up.
regards dawo



