# A variational construction of the TeichmÃ¼ller map

## Related Articles

- Large solutions for biharmonic maps in four dimensions. Angelsberg, Gilles // Calculus of Variations & Partial Differential Equations;Dec2007, Vol. 30 Issue 4, p417
We seek critical points of the Hessian energy functional $$E_\Omega(u)\!=\!\int_\Omega\vert\Delta u\vert^2dx$$ , where $$\Omega={\mathbb R}^4$$ or O is the unit disk $$B$$ in $${\mathbb R}^4$$ and u : O ? S 4. We show that $$E_{{\mathbb R}^4}$$ has a critical point which is not homotopic to the...

- Improved regularity of harmonic map flows with HÃ¶lder continuous energy. Topping, Peter // Calculus of Variations & Partial Differential Equations;Sep2004, Vol. 21 Issue 1, p47
For a smooth harmonic map flow u : M Ã— [0, T) â†’ N with blow-up as t â†‘ T, it has been asked [6,5,7] whether the weak limit u(T) M â†’ N is continuous. Recently, in [12], we showed that in general it need not be. Meanwhile, the energy function E(u(.)) [0, T) â†’ R,...

- Kinetical Inflation and Quintessence by F-Harmonic Map. Kanfon, Antonin; Lambert, Dominique // Journal of Modern Physics (21531196);Nov2012, Vol. 3 Issue 11, p1727
We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic maps. We showed that some F-harmonic map such as the trigonometric functions...

- Subelliptic harmonic maps from Carnot groups. Changyou Wang // Calculus of Variations & Partial Differential Equations;Sep2003, Vol. 18 Issue 1, p95
For subelliptic harmonic maps from a Carnot group into a Riemannian manifold without boundary, we prove that they are smooth near any $\epsilon$-regular point (see Definition 1.3) for sufficiently small $\epsilon > 0$. As a consequence, any stationary subelliptic harmonic map is smooth away from...

- On the Construction of Some New Harmonic Maps from â„[sup m] to â„[sup m]. Shi, Yuguang // Acta Mathematica Sinica;2001, Vol. 17 Issue 2, p301
Abstract. In this note, we construct some new harmonic maps from R[sup m] to H[sup m] via symmetric methods. Keywords Harmonic Maps, Symmetric Methods

- A dual monotonicity formula for harmonic mappings. Sumio Yamada // Calculus of Variations & Partial Differential Equations;Oct2003, Vol. 18 Issue 2, p181
The well-known monotonicity formula for harmonic maps says that the scaled energy functional over a ball of radius r is a non-decreasing function of r. The proof uses the fact that the energy functional is critical under any compactly supported variation on the domain of the map. In this...

- Linear Problems of Optimal Control of Fuzzy Maps. Plotnikov, Andrej V.; Komleva, Tatyana A. // Intelligent Information Management;Dec2009, Vol. 1 Issue 3, p139
In the present paper, we show the some properties of the fuzzy R-solution of the control linear fuzzy differential inclusions and research the optimal time problems for it

- Conservation laws for conformally invariant variational problems. Rivière, Tristan // Inventiones Mathematicae;Feb2007, Vol. 168 Issue 1, p1
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations,..., etc.) in divergence form. These divergence-free quantities generalize to target manifolds without symmetries the well known conservation laws for...

- Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra. Majumdar, A.; Robbins, J. M.; Zyskin, M. // Letters in Mathematical Physics;Nov2004, Vol. 70 Issue 2, p169
We derive a lower bound for energies of harmonic maps of convex polyhedra into the unit sphere S2 with tangent boundary conditions on the faces. We also establish that C8 maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent...