Regularity of the m-symphonic map
Regularity of the m-symphonic map
Abstract We introduce a new energy functional of conformal invariance and consider its critical points, named the m -symphonic map. We study a Hölder continuity of m -symphonic maps from domains of $$\mathbb {R}^m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>m</mml:mi></mml:msup></mml:math> into the spheres in the higher dimension $$m \ge 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>m</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> .