2 papers
math.GT2007
Equivalent metrics and compactifications
Young Deuk Kim
Let (X,d) be a metric space and m\in X. Suppose that ϕ:X\times X\to\mathbold{R} is a nonnegative symmetric function. We define a metric d^{ϕ,m} on X which is equivalent to d. If d^…
math.DG2007
Locally Euclidean metrics on R^3
Young Deuk Kim
For all 0<t \leq 1, we define a locally Euclidean metric ρ_t on R^3. These metrics are invariant under Euclidean isometries and, if t increases to 1, converges to the Euclidean met…