A Karcher saddle tower is a properly embedded singly periodic minimal surface without
boundary, whose quotient by its period, oriented vertically,
has genus 0 and 
Scherk-type ends, where 
is an integer. The ends
are asymptotic to vertical half-planes and become
flat annuli in the quotient. The family was constructed by Karcher (1988) as a generalization
of the singly periodic member of Scherk's
minimal surfaces, which corresponds to 
(Pérez and Traizet 2007). A symmetric example with
six Scherk-type ends in its periodic quotient is illustrated above.
Pérez and Traizet (2007) proved that every properly embedded singly periodic minimal surface without
boundary, with quotient genus
0 and 
Scherk-type ends, for 
, is either a Karcher saddle
tower or a singly periodic member of Scherk's
minimal surfaces.
The Karcher JE saddle tower belongs to a different, doubly periodic family with quotient genus 1 (Karcher and Palais 1999).
