##  [Mean Curvature](/mean-curvature) 

  ##  [Mean Curvature](https://natural.quantumdictionary.io/mean-curvature-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An extrinsic scalar measure of how a surface bends in ambient space, defined at a point as the average of the two principal curvatures, commonly H = (k1 + k2)/2; it equals half the trace of the shape operator.

 

 

 

 

 





 

 



 ##  [Mean Curvature](https://puremath.quantumdictionary.io/mean-curvature-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

At a regular point of a smooth surface, the arithmetic mean H=(k1+k2)/2 of the two principal curvatures; an extrinsic measure of local bending related to the surface's normal variation.