### Abstract

With {Mathematical expression}, we here construct, for each positive integer N, a smooth function {Mathematical expression} of degree zero so that there must be at least N singular points for any map that minimizes the energy {Mathematical expression} in the family {Mathematical expression}. The infimum of ε over U(g) is strictly smaller than the infimum of ε over the continuous functions in U(g). There are some generalizations to higher dimensions.

Original language | English (US) |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Manuscripta Mathematica |

Volume | 56 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1986 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*56*(1), 1-10. https://doi.org/10.1007/BF01171029

**A remark on H1 mappings.** / Hardt, Robert; Lin, Fang-Hua.

Research output: Contribution to journal › Article

*Manuscripta Mathematica*, vol. 56, no. 1, pp. 1-10. https://doi.org/10.1007/BF01171029

}

TY - JOUR

T1 - A remark on H1 mappings

AU - Hardt, Robert

AU - Lin, Fang-Hua

PY - 1986/3

Y1 - 1986/3

N2 - With {Mathematical expression}, we here construct, for each positive integer N, a smooth function {Mathematical expression} of degree zero so that there must be at least N singular points for any map that minimizes the energy {Mathematical expression} in the family {Mathematical expression}. The infimum of ε over U(g) is strictly smaller than the infimum of ε over the continuous functions in U(g). There are some generalizations to higher dimensions.

AB - With {Mathematical expression}, we here construct, for each positive integer N, a smooth function {Mathematical expression} of degree zero so that there must be at least N singular points for any map that minimizes the energy {Mathematical expression} in the family {Mathematical expression}. The infimum of ε over U(g) is strictly smaller than the infimum of ε over the continuous functions in U(g). There are some generalizations to higher dimensions.

UR - http://www.scopus.com/inward/record.url?scp=0002135323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002135323&partnerID=8YFLogxK

U2 - 10.1007/BF01171029

DO - 10.1007/BF01171029

M3 - Article

AN - SCOPUS:0002135323

VL - 56

SP - 1

EP - 10

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -