Math 583
Homework due May 12
Part 2
Problem 4: Let Σ ⊂Rnbe such that ∀Q∈Σ
(1) lim
r→0βΣ(Q, r) = 0 where βΣ(Q, r) = inf
L∈G(n,n−1) sup
y∈B(Q,r)∩Σ
d(y, L)
r.
Prove that
(2) dimHΣ≤n−1.
1
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Homework Problem - Special Topics | MATH 583, Assignments of Mathematics
Material Type: Assignment; Professor: Toro; Class: SPECIAL TOPICS; Subject: Mathematics; University: University of Washington - Seattle; Term: Spring 2008;
Typology: Assignments
Pre 2010
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Math 583
Homework due May 12
Part 2
Problem 4: Let Σ ⊂ Rn^ be such that ∀Q ∈ Σ
(1) (^) rlim→ 0 βΣ(Q, r) = 0 where βΣ(Q, r) = (^) L∈Ginf(n,n−1) (^) y∈Bsup(Q,r)∩Σ^ d(y, L r ).
Prove that (2) dimH Σ ≤ n − 1.