  Solutions of Einstein's equations are found for global defects in a
higher-dimensional spacetime with a nonzero cosmological constant Lambda. The
defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field
configuration in the n extra dimensions. For Lambda = 0 and n > 2, the
solutions are characterized by a flat brane worldsheet and a solid angle
deficit in the extra dimensions. For Lambda > 0, one class of solutions
describes spherical branes in an inflating higher-dimensional universe.
Instantons obtained by a Euclidean continuation of such solutions describe
quantum nucleation of the entire inflating brane-world, or of a spherical brane
in an inflating higher-dimensional universe. For Lambda < 0, one class of
solutions exhibits an exponential warp factor. It is similar to spacetimes
previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.
