Lipschitz geometry and combinatorics of abnormal surface germs

Lipschitz geometry of pairs of normally embedded Hölder triangles

“…However, Theorem 3.20 below states that conditions of Proposition 3.2 are satisfied if T is elementary with respect to f and (3.1) holds. The following proposition from [6] is an important step in the proof of Theorem 3.20.…”

Lipschitz geometry of pairs of normally embedded Hölder triangles

“…However, Theorem 3.18 below states that conditions of Proposition 3.2 are satisfied if T is elementary with respect to f and (5) holds. The following Proposition from [4] is an important step in the proof of Theorem 3.18.…”

“…Case 4. Using the same arguments as in the proof of [4,Proposition 2.20], we assume that T ′ = T β ⊂ R 2 is a standard β-Hölder triangle (1), T ∪ T ′ ⊂ R n , and π : T → R 2 is an orthogonal projection. We may also assume that Q is not a point, and that µ(q 1 ), where q 1 = tord(γ 1 , T ′ ), is the maximal value of µ(q) for q ∈ Q.…”

“…Another important step was made in [4], where an "abnormal" semialgebraic surface germ was canonically partitioned into normally embedded Hölder triangles. Several constructions and results from [4] are used in the present paper.…”