Liouville's theorem | Hopf link | Chinese remainder theorem | Karl Hopf | Hopf algebra | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem |
While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds.
In 1931 Hans Hopf and his student Rinow published the Hopf-Rinow theorem in their article "Über den Begriff der vollständigen differentialgeometrischen Fläche".
Dirk Kreimer (born 1960) is a German physicist who pioneered the Hopf-algebraic approach to quantum field theory with Alain Connes and other co-authors.
Several explanations have been suggested by biologists including W. D. Hamilton, Alexey Kondrashov, George C. Williams, Harris Bernstein, Carol Bernstein, Michael M. Cox, Frederic A. Hopf and Richard E. Michod to explain how sexual reproduction is maintained in a vast array of different living organisms.
In the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.
Karl Hopf (Hamm, Westphalia, February 19, 1832 – Wiesbaden, August 23, 1873) or Carl Hermann Friedrich Johann Hopf was historian and expert in Medieval Greece, both Byzantine and Frankish.