Legal Question in Real Estate Law in California

You can ask your neighbor to do so, but he has no obligation to do it.

Sure, you can ask. You probably mean can you demand that he do so, as a matter of right. That is a more complicated and difficult-to-answer question.

In California, the rule is that limbs and roots of trees that cross the property line constitute a trespass, and the victim of the trespass is entitled to a self-help remedy, i.e., may cut the offending limbs or roots at the property line, at his own expense, but only if it can be done without additional harm such as killing the tree or creating a windstorm hazard. In addition, the limbs or roots may constitute a private nuisance (Civil Code sections 3479, 3481).

In your case, however, I assume that the trees do not extend over the property line, or at least do not to any significant extent. That being the case, there is no trespass at this point.

Research shows that in theory you might have a remedy: an injunction; IF the risk from the trees interferes with your "use and enjoyment" of the property. Even a presently-slight interference might qualify, as it will increase with growth of the tree. See Shevlin v. Johnston (1922) 56 Cal.App. 563 at p. 565; also Lindsay-Strathmore Irrigation District v. Superior Court of Tulare County (1920) 182 Cal. 315 at p. 326. There are other old cases as well. However, on the whole, you'd have a much cleaner case in court if you have suffered actual damage, not just a threat of harm in the next big storm.

This is knd of a theoretical answer. As a practical matter, I think you should discuss the trees with your neighbor as a potential hazard, remind him of his potential liability for any damage done, and see if you can arrive at some voluntary solution. You might suggest hiring a licensed arborist to come out and evaluate the risks -- they may be lesser or perhaps greater than either of you think. An arborist could also recommend trimming practices that would maximize safety without harming the trees or reducing their attractiveness.