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A Liouville Theorem for Harmonic Maps
American Journal of Mathematics, 1995The main result of the author is a Liouville type theorem for harmonic maps with domain \(M\), a complete Riemannian manifold of nonnegative Ricci curvature, and range \(N\), a simply-connected complete Riemannian manifold with sectional curvature bounded above by \(-a^2\), \(a>0\).
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The Poincar�?Lyapunov?Liouville?Arnol'd theorem
Functional Analysis and Its Applications, 1994The author presents the following theorem: Let \(M\) be a symplectic manifold of dimension \(2n\). Suppose that a Hamiltonian flow \(X_H\), \(H \in C^\infty (M)\), possesses \(k\) \((1 \leq k \leq n)\) integrals in involution \(H= F_1,F_2,\dots, F_k\) and that there exists a \(k\)-dimensional compact connected submanifold \(S \subset M\) invariant ...
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1997
Proceeding del Meeting Reaction Diffusion Systems, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc.
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Proceeding del Meeting Reaction Diffusion Systems, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc.
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A Strong Version of Liouville's Theorem
The American Mathematical Monthly, 20081. THE MAIN RESULT. Liouville's theorem states that every bounded holomor phic function on C is constant. Let us recall that holomorphic functions / on open subsets U of the complex plane have the mean value property, that is, for every closed disk B(z,r) in U, the value of / at its center z is equal to the average of the values of f on the circle S(z ...
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Phragmen-Liouville-type theorems and Liouville theorems for a linear parabolic equation
Mathematical Notes of the Academy of Sciences of the USSR, 1985The author proves some results of Phragmén-Lindelöf type and some Liouville type theorems applying to a class of linear parabolic equations with measurable coefficients.
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Another Approach to Liouville Theorem
Mathematische Nachrichten, 1982Bojarski, B., Iwaniec, T.
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A Liouville-type theorem for the stationary MHD equations
Nonlinear Analysis: Real World Applications, 2023Minsuk Yang, Jiří Neustupa
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A Liouville-type theorem for the stationary Navier–Stokes equations
Applied Mathematics Letters, 2023Youseung Cho, Jongkeun Choi, Minsuk Yang
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