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 Apr 7 awarded Popular Question Feb 18 awarded Popular Question Dec 12 comment Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function @user123 assume $f$ is nonconstant, holomorphic on $D$ and continuous on $\bar{D}$, with $f$ nonvanishing on $D$, ... then use the minimum modulus principle we effectively just showed in the previous problem to get a contradiction Dec 12 comment Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function @user123 The maximum of $f$ on the closure of $D$ is the maximum on the boundary by the maximum modulus principle, and because $\bar{D}$ is compact. Comsidering $g=1/f$, we see $g$ has the same property, and hence $f$ attains both its maximum and minimum on the boundary. Since $f$ is constant there, by the open mapping theorem, we have $f$ is constant. Oct 29 accepted On the dual face of a subset of a convex cone Oct 29 comment On the dual face of a subset of a convex cone It's the third dual of $F$. And now that you mention it, I think it follows from the definition. My bad. Oct 29 revised On the dual face of a subset of a convex cone added details Oct 29 revised On the dual face of a subset of a convex cone typo Oct 29 asked On the dual face of a subset of a convex cone Oct 26 accepted On the range of positive semidefinite matrices Oct 26 asked On the range of positive semidefinite matrices Oct 15 awarded Popular Question Oct 8 awarded Popular Question Oct 7 awarded Yearling Jul 20 awarded Notable Question Jun 11 awarded Notable Question Jun 4 revised Estimate for the power of a integral added information Jun 4 answered Estimate for the power of a integral May 17 awarded Nice Question Apr 10 accepted On closed ranges and sequences which converge to zero