O‐minimal total harmonic functions are polynomial

Key Points

• This research aims to prove that harmonic functions definable in o-minimal expansions of the real field are polynomial.
• Investigated harmonic functions within the context of o-minimal structures.
• Analyzed the definability of these functions in mathematical terms based on existing theories.
• Established that any harmonic function in the specified context must be a polynomial function.
• Demonstrated that the conditions of o-minimality directly imply polynomial behavior.