## An identity related to generalized divergence theorem

I am trying to verify one proposition proved in Reilly’s paper. For the notation of this, please consult the paper.

**Propsotion 2.4** Let be a domain in . is a smooth function on . Then

**Proof:** Take an orthonormal frame field such that is tangent to . Notice

where . It follows from Remark 2.3 that

where is the outward unit normal to . Changing the coordinates to and , we can get

It is easy to see

and

Therefore the proposition is established.

Remark: Robert Reilly, On the hessian of a function and the curvature of its graph

### Like this:

Like Loading...

*Related*

or leave a trackback:

Trackback URL.