### Abstract

The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂ M an open domain and f: Ω → ℝ a harmonic function. Then f is Lipschitz on any compact subset of. Ω Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

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

Pages (from-to) | 135-141 |

Number of pages | 7 |

Journal | Electronic Research Announcements of the American Mathematical Society |

Volume | 9 |

Issue number | 17 |

DOIs | |

State | Published - Dec 17 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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**Harmonic functions on alexandrov spaces and their applications.** / Petrunin, Anton.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Harmonic functions on alexandrov spaces and their applications

AU - Petrunin, Anton

PY - 2003/12/17

Y1 - 2003/12/17

N2 - The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂ M an open domain and f: Ω → ℝ a harmonic function. Then f is Lipschitz on any compact subset of. Ω Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

AB - The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂ M an open domain and f: Ω → ℝ a harmonic function. Then f is Lipschitz on any compact subset of. Ω Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

UR - http://www.scopus.com/inward/record.url?scp=15944370025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15944370025&partnerID=8YFLogxK

U2 - 10.1090/S1079-6762-03-00120-3

DO - 10.1090/S1079-6762-03-00120-3

M3 - Article

VL - 9

SP - 135

EP - 141

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

SN - 1935-9179

IS - 17

ER -