constitutional conviction

Assume you are a judge in state court presiding over a high-profile criminal case in which the governor, who is married and has five children, allegedly killed his campaign manager (who was also his mistress) because she wanted to break off their relationship. The case has generated tremendous publicity in the local and national media. Discuss the following: (a) what constitutional issues might arise during the trial, given the nature of the case; and (b) what you, as the trial judge, can do to avoid the conviction being reversed by the U.S. Supreme Court on those issues if raised on appeal. Support your response.